Cao, Zhenbang; Grebogi, Celso; Li, Denghui; Xie, Jianhua The existence of Aubry-Mather sets for the Fermi-Ulam model. (English) Zbl 07314137 Qual. Theory Dyn. Syst. 20, No. 1, Paper No. 12, 12 p. (2021). MSC: 37E40 37E45 37N05 37J46 70H12 PDF BibTeX XML Cite \textit{Z. Cao} et al., Qual. Theory Dyn. Syst. 20, No. 1, Paper No. 12, 12 p. (2021; Zbl 07314137) Full Text: DOI
Zhang, Ke On the tangent cones of Aubry sets. (English. French summary) Zbl 1448.37069 Ann. Fac. Sci. Toulouse, Math. (6) 29, No. 1, 27-38 (2020). Reviewer: William J. Satzer Jr. (St. Paul) MSC: 37J39 37J51 37J06 37J40 PDF BibTeX XML Cite \textit{K. Zhang}, Ann. Fac. Sci. Toulouse, Math. (6) 29, No. 1, 27--38 (2020; Zbl 1448.37069) Full Text: DOI
Cheng, Chong-Qing; Xue, Jinxin Variational approach to Arnold diffusion. (English) Zbl 1427.37049 Sci. China, Math. 62, No. 11, 2103-2130 (2019). MSC: 37J40 37J51 49L25 PDF BibTeX XML Cite \textit{C.-Q. Cheng} and \textit{J. Xue}, Sci. China, Math. 62, No. 11, 2103--2130 (2019; Zbl 1427.37049) Full Text: DOI
Hu, Sen On John Mather’s work. (English) Zbl 1430.32011 Methods Appl. Anal. 25, No. 4, 291-306 (2018). MSC: 32S60 37J40 37J51 57R20 57R30 57R32 57R45 01A70 PDF BibTeX XML Cite \textit{S. Hu}, Methods Appl. Anal. 25, No. 4, 291--306 (2018; Zbl 1430.32011) Full Text: DOI
Siconolfi, Antonio; Zabad, Sahar Scalar reduction techniques for weakly coupled Hamilton-Jacobi systems. (English) Zbl 1415.35094 NoDEA, Nonlinear Differ. Equ. Appl. 25, No. 6, Paper No. 50, 20 p. (2018). MSC: 35F21 49L25 37J50 35D40 35Q93 PDF BibTeX XML Cite \textit{A. Siconolfi} and \textit{S. Zabad}, NoDEA, Nonlinear Differ. Equ. Appl. 25, No. 6, Paper No. 50, 20 p. (2018; Zbl 1415.35094) Full Text: DOI
Qin, Wen-Xin; Wang, Ya-Nan Denjoy minimal sets and Birkhoff periodic orbits for non-exact monotone twist maps. (English) Zbl 1385.37058 J. Differ. Equations 264, No. 11, 7006-7021 (2018). MSC: 37E40 37C65 70F45 PDF BibTeX XML Cite \textit{W.-X. Qin} and \textit{Y.-N. Wang}, J. Differ. Equations 264, No. 11, 7006--7021 (2018; Zbl 1385.37058) Full Text: DOI
Arnaud, Marie-Claude; Le Calvez, Patrice A notion of Denjoy sub-system. (Une notion de sous-système de Denjoy.) (English. Abridged French version) Zbl 1379.37059 C. R., Math., Acad. Sci. Paris 355, No. 8, 914-919 (2017). MSC: 37C55 37E40 37E45 37J50 PDF BibTeX XML Cite \textit{M.-C. Arnaud} and \textit{P. Le Calvez}, C. R., Math., Acad. Sci. Paris 355, No. 8, 914--919 (2017; Zbl 1379.37059) Full Text: DOI
Garibaldi, Eduardo; Gomes, João Tiago Assunção Aubry set for asymptotically sub-additive potentials. (English) Zbl 1357.37006 Stoch. Dyn. 16, No. 2, Article ID 1660009, 13 p. (2016). Reviewer: Thomas B. Ward (Leeds) MSC: 37A30 37A05 37A50 37B10 PDF BibTeX XML Cite \textit{E. Garibaldi} and \textit{J. T. A. Gomes}, Stoch. Dyn. 16, No. 2, Article ID 1660009, 13 p. (2016; Zbl 1357.37006) Full Text: DOI
Davini, Andrea; Siconolfi, Antonio Existence and regularity of strict critical subsolutions in the stationary ergodic setting. (English) Zbl 1336.35114 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 33, No. 2, 243-272 (2016). MSC: 35F21 35D40 35B27 49L25 PDF BibTeX XML Cite \textit{A. Davini} and \textit{A. Siconolfi}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 33, No. 2, 243--272 (2016; Zbl 1336.35114) Full Text: DOI arXiv
Piatnitski, A.; Rybalko, A.; Rybalko, V. Singularly perturbed spectral problems with Neumann boundary conditions. (English) Zbl 1342.35024 Complex Var. Elliptic Equ. 61, No. 2, 252-274 (2016). MSC: 35B25 35B40 35P15 35J25 PDF BibTeX XML Cite \textit{A. Piatnitski} et al., Complex Var. Elliptic Equ. 61, No. 2, 252--274 (2016; Zbl 1342.35024) Full Text: DOI
Fathi, Albert Time functions revisited. (English) Zbl 1335.53096 Int. J. Geom. Methods Mod. Phys. 12, No. 8, Article ID 1560027, 12 p. (2015). Reviewer: Viviana del Barco (Rosario) MSC: 53C50 PDF BibTeX XML Cite \textit{A. Fathi}, Int. J. Geom. Methods Mod. Phys. 12, No. 8, Article ID 1560027, 12 p. (2015; Zbl 1335.53096) Full Text: DOI
Gidea, Marian Global diffusion on a tight three-sphere. (English) Zbl 1394.37096 Qual. Theory Dyn. Syst. 14, No. 2, 227-263 (2015). Reviewer: Božidar Jovanović (Beograd) MSC: 37J40 37C50 37J05 37J55 53D10 37J25 PDF BibTeX XML Cite \textit{M. Gidea}, Qual. Theory Dyn. Syst. 14, No. 2, 227--263 (2015; Zbl 1394.37096) Full Text: DOI arXiv
Fathi, Albert; Pageault, Pierre Aubry-Mather theory for homeomorphisms. (English) Zbl 1343.37012 Ergodic Theory Dyn. Syst. 35, No. 4, 1187-1207 (2015). Reviewer: Zdzisław Dzedzej (Gdansk) MSC: 37B25 37B20 37B35 PDF BibTeX XML Cite \textit{A. Fathi} and \textit{P. Pageault}, Ergodic Theory Dyn. Syst. 35, No. 4, 1187--1207 (2015; Zbl 1343.37012) Full Text: DOI
Figalli, A.; Rifford, L. Closing Aubry sets. II. (English) Zbl 1377.37090 Commun. Pure Appl. Math. 68, No. 3, 345-412 (2015). Reviewer: William J. Satzer Jr. (St. Paul) MSC: 37J50 37J45 PDF BibTeX XML Cite \textit{A. Figalli} and \textit{L. Rifford}, Commun. Pure Appl. Math. 68, No. 3, 345--412 (2015; Zbl 1377.37090) Full Text: DOI
Cui, Xiaojun On commuting Tonelli Hamiltonians: time-periodic case. (English) Zbl 1334.37060 Acta Math. Sin., Engl. Ser. 30, No. 10, 1698-1718 (2014). Reviewer: Antonio De Nicola (Coimbra) MSC: 37J35 49L25 35F21 37J50 PDF BibTeX XML Cite \textit{X. Cui}, Acta Math. Sin., Engl. Ser. 30, No. 10, 1698--1718 (2014; Zbl 1334.37060) Full Text: DOI arXiv
Wang, Ya-Nan; Qin, Wen-Xin Many Denjoy minimal sets for monotone recurrence relations. (English) Zbl 1350.37015 Nonlinearity 27, No. 9, 2393-2408 (2014). MSC: 37B20 37C65 37E40 PDF BibTeX XML Cite \textit{Y.-N. Wang} and \textit{W.-X. Qin}, Nonlinearity 27, No. 9, 2393--2408 (2014; Zbl 1350.37015) Full Text: DOI
Wang, Ya-Nan; Qin, Wen-Xin A necessary condition of nonminimal aubry-mather sets for monotone recurrence relations. (English) Zbl 1284.37023 Int. J. Bifurcation Chaos Appl. Sci. Eng. 24, No. 1, Article ID 1450012, 8 p. (2014). MSC: 37C55 37B20 37E45 PDF BibTeX XML Cite \textit{Y.-N. Wang} and \textit{W.-X. Qin}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 24, No. 1, Article ID 1450012, 8 p. (2014; Zbl 1284.37023) Full Text: DOI
Reich, Simeon; Zaslavski, Alexander J. Genericity in nonlinear analysis. (English) Zbl 1296.47002 Developments in Mathematics 34. New York, NY: Springer (ISBN 978-1-4614-9532-1/hbk; 978-1-4614-9533-8/ebook). xiii, 520 p. (2014). Reviewer: Barry Turett (Rochester) MSC: 47-02 47H10 47H09 46E30 41A65 54H25 54E50 PDF BibTeX XML Cite \textit{S. Reich} and \textit{A. J. Zaslavski}, Genericity in nonlinear analysis. New York, NY: Springer (2014; Zbl 1296.47002) Full Text: DOI
Figalli, A.; Rifford, L. Aubry sets, Hamilton-Jacobi equations, and the Mañé conjecture. (English) Zbl 1364.37137 Ghomi, Mohammad (ed.) et al., Geometric analysis, mathematical relativity, and nonlinear partial differential equations. Proceedings of the southeast geometry seminars held at Emory University, Atlanta, GA, the Georgia Institute of Technology, Atlanta, GA, the University of Alabama, Birmingham, AL and the University of Tennessee, Knoxville, TN, USA, 2009 – 2011. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-9149-0/pbk; 978-1-4704-1081-0/ebook). Contemporary Mathematics 599, 83-104 (2013). Reviewer: Patrick Bernard (Paris) MSC: 37J50 35F21 PDF BibTeX XML Cite \textit{A. Figalli} and \textit{L. Rifford}, Contemp. Math. 599, 83--104 (2013; Zbl 1364.37137) Full Text: DOI
Rifford, Ludovic Regularity of weak KAM solutions and Mañé’s conjecture. (English) Zbl 1321.37058 Sémin. Laurent Schwartz, EDP Appl. 2011-2012, Exp. No. XXVII, 22 p. (2013). Reviewer: William J. Satzer jun. (St. Paul) MSC: 37J40 37K55 70H08 PDF BibTeX XML Cite \textit{L. Rifford}, Sémin. Laurent Schwartz, EDP Appl. 2011--2012, Exp. No. XXVII, 22 p. (2013; Zbl 1321.37058) Full Text: DOI
Fathi, Albert Weak KAM from a PDE point of view: viscosity solutions of the Hamilton-Jacobi equation and Aubry set. (English) Zbl 1297.35004 Proc. R. Soc. Edinb., Sect. A, Math. 142, No. 6, 1193-1236 (2012). Reviewer: Laurent Thomann (Nantes) MSC: 35-02 35F21 49L25 35D40 37K55 35B35 PDF BibTeX XML Cite \textit{A. Fathi}, Proc. R. Soc. Edinb., Sect. A, Math. 142, No. 6, 1193--1236 (2012; Zbl 1297.35004) Full Text: DOI
Wang, Xiaoming Aubry-Mather sets for a class of superlinear asymmetric Duffing equations. (Chinese. English summary) Zbl 1274.34113 Chin. Ann. Math., Ser. A 33, No. 3, 351-358 (2012). MSC: 34C15 37C55 34C20 PDF BibTeX XML Cite \textit{X. Wang}, Chin. Ann. Math., Ser. A 33, No. 3, 351--358 (2012; Zbl 1274.34113)
Barles, Guy; Ishii, Hitoshi; Mitake, Hiroyoshi On the large time behavior of solutions of Hamilton-Jacobi equations associated with nonlinear boundary conditions. (English) Zbl 1282.70037 Arch. Ration. Mech. Anal. 204, No. 2, 515-558 (2012). MSC: 70H20 35Q70 49L25 PDF BibTeX XML Cite \textit{G. Barles} et al., Arch. Ration. Mech. Anal. 204, No. 2, 515--558 (2012; Zbl 1282.70037) Full Text: DOI arXiv
Wang, Kaizhi; Yan, Jun The rate of convergence of new Lax-Oleinik type operators for time-periodic positive definite Lagrangian systems. (English) Zbl 1276.37044 Nonlinearity 25, No. 7, 2039-2057 (2012). Reviewer: Daniel Massart (Montpellier) MSC: 37J50 70G75 35F21 PDF BibTeX XML Cite \textit{K. Wang} and \textit{J. Yan}, Nonlinearity 25, No. 7, 2039--2057 (2012; Zbl 1276.37044) Full Text: DOI arXiv
Davini, Andrea; Siconolfi, Antonio Weak KAM theory topics in the stationary ergodic setting. (English) Zbl 1271.37041 Calc. Var. Partial Differ. Equ. 44, No. 3-4, 319-350 (2012). Reviewer: Andrea Pascucci (Bologna) MSC: 37J40 35B27 35D40 35F21 49L25 37K55 PDF BibTeX XML Cite \textit{A. Davini} and \textit{A. Siconolfi}, Calc. Var. Partial Differ. Equ. 44, No. 3--4, 319--350 (2012; Zbl 1271.37041) Full Text: DOI arXiv
Mramor, Blaz; Rink, Bob Ghost circles in lattice Aubry-Mather theory. (English) Zbl 1253.37062 J. Differ. Equations 252, No. 4, 3163-3208 (2012). MSC: 37J50 37K60 82B20 PDF BibTeX XML Cite \textit{B. Mramor} and \textit{B. Rink}, J. Differ. Equations 252, No. 4, 3163--3208 (2012; Zbl 1253.37062) Full Text: DOI arXiv
Wang, Xiaoming Aubry-Mather sets for a class of superlinear Duffing equations. (Chinese. English summary) Zbl 1249.34122 Math. Appl. 24, No. 4, 659-664 (2011). MSC: 34C15 34C25 37C55 PDF BibTeX XML Cite \textit{X. Wang}, Math. Appl. 24, No. 4, 659--664 (2011; Zbl 1249.34122)
Capietto, Anna; Soave, Nicola Some remarks on Mather’s theorem and Aubry-Mather sets. (English) Zbl 1237.37045 Commun. Appl. Anal. 15, No. 2-4, 283-298 (2011). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37J50 PDF BibTeX XML Cite \textit{A. Capietto} and \textit{N. Soave}, Commun. Appl. Anal. 15, No. 2--4, 283--298 (2011; Zbl 1237.37045)
Massart, Daniel Aubry sets vs. Mather sets in two degrees of freedom. (English) Zbl 1254.37043 Calc. Var. Partial Differ. Equ. 42, No. 3-4, 429-460 (2011). MSC: 37J50 PDF BibTeX XML Cite \textit{D. Massart}, Calc. Var. Partial Differ. Equ. 42, No. 3--4, 429--460 (2011; Zbl 1254.37043) Full Text: DOI arXiv
Bernard, Patrick; Oliveira dos Santos, Joana A geometric definition of the Aubry – Mather set. (English) Zbl 1200.37055 J. Topol. Anal. 2, No. 3, 385-393 (2010). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37J50 37J05 53D12 57R17 PDF BibTeX XML Cite \textit{P. Bernard} and \textit{J. Oliveira dos Santos}, J. Topol. Anal. 2, No. 3, 385--393 (2010; Zbl 1200.37055) Full Text: DOI
Capietto, Anna; Dambrosio, Walter; Wang, Xinping Quasi-periodic solutions of a damped reversible oscillator at resonance. (English) Zbl 1240.34221 Differ. Integral Equ. 22, No. 9-10, 1033-1046 (2009). Reviewer: Milan Tvrdý (Praha) MSC: 34C27 37E40 37E45 PDF BibTeX XML Cite \textit{A. Capietto} et al., Differ. Integral Equ. 22, No. 9--10, 1033--1046 (2009; Zbl 1240.34221)
Osuna, Osvaldo The Aubry set for periodic Lagrangians on the circle. (English) Zbl 1175.37068 Bull. Braz. Math. Soc. (N.S.) 40, No. 2, 247-252 (2009). MSC: 37J50 PDF BibTeX XML Cite \textit{O. Osuna}, Bull. Braz. Math. Soc. (N.S.) 40, No. 2, 247--252 (2009; Zbl 1175.37068) Full Text: DOI
Mitake, Hiroyoshi Large time behavior of solutions of Hamilton-Jacobi equations with periodic boundary data. (English) Zbl 1184.35061 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 11, 5392-5405 (2009). Reviewer: Vasile Iftode (Bucureşti) MSC: 35B40 35B10 35F25 35F30 PDF BibTeX XML Cite \textit{H. Mitake}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 11, 5392--5405 (2009; Zbl 1184.35061) Full Text: DOI
Iturriaga, Renato; Sánchez-Morgado, Héctor Hyperbolicity and exponential convergence of the Lax-Oleinik semigroup. (English) Zbl 1163.37021 J. Differ. Equations 246, No. 5, 1744-1753 (2009). Reviewer: Jan Andres (Olomouc) MSC: 37J50 49L25 70H20 PDF BibTeX XML Cite \textit{R. Iturriaga} and \textit{H. Sánchez-Morgado}, J. Differ. Equations 246, No. 5, 1744--1753 (2009; Zbl 1163.37021) Full Text: DOI
Mitake, Hiroyoshi The large-time behavior of solutions of the Cauchy-Dirichlet problem for Hamilton-Jacobi equations. (English) Zbl 1171.35332 NoDEA, Nonlinear Differ. Equ. Appl. 15, No. 3, 347-362 (2008). Reviewer: Vasile Iftode (Bucureşti) MSC: 35B40 35F25 35F30 PDF BibTeX XML Cite \textit{H. Mitake}, NoDEA, Nonlinear Differ. Equ. Appl. 15, No. 3, 347--362 (2008; Zbl 1171.35332) Full Text: DOI
Roquejoffre, Jean-Michel Qualitative properties of solutions of Hamilton-Jacobi equations (after A. Fathi, A. Siconolfi, P. Bernard). (Propriétés qualitatives des solutions des équations de Hamilton-Jacobi (d’après A. Fathi, A. Siconolfi, P. Bernard).) (French) Zbl 1162.35003 Séminaire Bourbaki. Volume 2006/2007. Exposés 967–981. Paris: Société Mathématique de France (ISBN 978-2-85629-253-2/pbk). Astérisque 317, 269-294, Exp. No. 975 (2008). Reviewer: Vasile Iftode (Bucureşti) MSC: 35F30 37J50 49L25 35A02 35B65 35C15 35D40 70H20 PDF BibTeX XML Cite \textit{J.-M. Roquejoffre}, Astérisque 317, 269--294, Exp. No. 975 (2008; Zbl 1162.35003) Full Text: Link
Yamaguchi, Yoshihiro; Tanikawa, Kiyotaka On Mather’s connecting orbits in standard mapping. (English) Zbl 1153.37030 Prog. Theor. Phys. 119, No. 4, 533-559 (2008). MSC: 37J50 PDF BibTeX XML Cite \textit{Y. Yamaguchi} and \textit{K. Tanikawa}, Prog. Theor. Phys. 119, No. 4, 533--559 (2008; Zbl 1153.37030) Full Text: DOI
Arnaud, Marie-Claude The tiered Aubry set for autonomous Lagrangian functions. (English) Zbl 1152.37025 Ann. Inst. Fourier 58, No. 5, 1733-1759 (2008). Reviewer: William J. Satzer jun. (St. Paul) MSC: 37J45 37J50 37C20 PDF BibTeX XML Cite \textit{M.-C. Arnaud}, Ann. Inst. Fourier 58, No. 5, 1733--1759 (2008; Zbl 1152.37025) Full Text: DOI Numdam EuDML
Cui, Xiaojun Dynamics near an isolated \(\tilde M\)-semi-static homoclinic orbit. (English) Zbl 1160.37391 J. Math. Anal. Appl. 340, No. 2, 854-860 (2008). Reviewer: Messoud A. Efendiev (Berlin) MSC: 37J50 34C25 37C29 37J45 PDF BibTeX XML Cite \textit{X. Cui}, J. Math. Anal. Appl. 340, No. 2, 854--860 (2008; Zbl 1160.37391) Full Text: DOI
Liang, Xue; Chen, Cui On Mañé set and Aubry set. (English) Zbl 1150.37379 Northeast. Math. J. 23, No. 5, 433-443 (2007). MSC: 37J50 37N10 37J40 PDF BibTeX XML Cite \textit{X. Liang} and \textit{C. Chen}, Northeast. Math. J. 23, No. 5, 433--443 (2007; Zbl 1150.37379)
Bernard, Patrick Existence of \(C^{1,1}\) critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds. (English. French summary) Zbl 1133.35027 Ann. Sci. Éc. Norm. Supér. (4) 40, No. 3, 445-452 (2007). MSC: 35F25 58J99 49L99 35D05 PDF BibTeX XML Cite \textit{P. Bernard}, Ann. Sci. Éc. Norm. Supér. (4) 40, No. 3, 445--452 (2007; Zbl 1133.35027) Full Text: DOI Numdam EuDML
Bernard, Patrick Smooth critical sub-solutions of the Hamilton-Jacobi equation. (English) Zbl 1125.37044 Math. Res. Lett. 14, No. 3, 503-511 (2007). MSC: 37J50 37J40 70H20 37D05 PDF BibTeX XML Cite \textit{P. Bernard}, Math. Res. Lett. 14, No. 3, 503--511 (2007; Zbl 1125.37044) Full Text: DOI
Serea, Oana-Silvia Viscosity solutions for partial differential equations with Neumann type boundary conditions and some aspects of Aubry-Mather theory. (English) Zbl 1152.49026 J. Math. Anal. Appl. 336, No. 1, 664-682 (2007). Reviewer: Vasile Iftode (Bucureşti) MSC: 49K24 35F20 37J50 49L25 PDF BibTeX XML Cite \textit{O.-S. Serea}, J. Math. Anal. Appl. 336, No. 1, 664--682 (2007; Zbl 1152.49026) Full Text: DOI
Davini, Andrea; Siconolfi, Antonio A generalized dynamical approach to the large time behavior of solutions of Hamilton–Jacobi equations. (English) Zbl 1109.49034 SIAM J. Math. Anal. 38, No. 2, 478-502 (2006). MSC: 49L25 35B40 58J37 37J50 PDF BibTeX XML Cite \textit{A. Davini} and \textit{A. Siconolfi}, SIAM J. Math. Anal. 38, No. 2, 478--502 (2007; Zbl 1109.49034) Full Text: DOI
Bernard, Patrick Symplectic aspects of Mather theory. (English) Zbl 1114.37036 Duke Math. J. 136, No. 3, 401-420 (2007). Reviewer: Maria Saprykina (Kingston) MSC: 37J50 PDF BibTeX XML Cite \textit{P. Bernard}, Duke Math. J. 136, No. 3, 401--420 (2007; Zbl 1114.37036)
Zheng, Yong; Cheng, Chong-Qing Homoclinic orbits of positive definite Lagrangian systems. (English) Zbl 1104.37042 J. Differ. Equations 229, No. 1, 297-316 (2006). MSC: 37J45 37J50 PDF BibTeX XML Cite \textit{Y. Zheng} and \textit{C.-Q. Cheng}, J. Differ. Equations 229, No. 1, 297--316 (2006; Zbl 1104.37042) Full Text: DOI
Rorro, M. An approximation scheme for the effective Hamiltonian and applications. (English) Zbl 1100.65058 Appl. Numer. Math. 56, No. 9, 1238-1254 (2006). Reviewer: Jan Lovíšek (Bratislava) MSC: 65K10 49L25 49M25 PDF BibTeX XML Cite \textit{M. Rorro}, Appl. Numer. Math. 56, No. 9, 1238--1254 (2006; Zbl 1100.65058) Full Text: DOI
Anantharaman, Nalini; Iturriaga, Renato; Padilla, Pablo; Sánchez-Morgado, Héctor Physical solutions of the Hamilton-Jacobi equation. (English) Zbl 1081.37036 Discrete Contin. Dyn. Syst., Ser. B 5, No. 3, 513-528 (2005). MSC: 37J50 49L25 70H20 PDF BibTeX XML Cite \textit{N. Anantharaman} et al., Discrete Contin. Dyn. Syst., Ser. B 5, No. 3, 513--528 (2005; Zbl 1081.37036) Full Text: DOI
Cui, Xiaojun; Cheng, Chong-Qing; Cheng, Wei Existence of infinitely many homoclinic orbits to Aubry sets for positive definite Lagrangian systems. (English) Zbl 1066.37011 J. Differ. Equations 214, No. 1, 176-188 (2005). MSC: 37C29 PDF BibTeX XML Cite \textit{X. Cui} et al., J. Differ. Equations 214, No. 1, 176--188 (2005; Zbl 1066.37011) Full Text: DOI
Mather, John N. Examples of Aubry sets. (English) Zbl 1090.37047 Ergodic Theory Dyn. Syst. 24, No. 5, 1667-1723 (2004). Reviewer: Jens Rademacher (Berlin) MSC: 37J50 37J40 PDF BibTeX XML Cite \textit{J. N. Mather}, Ergodic Theory Dyn. Syst. 24, No. 5, 1667--1723 (2004; Zbl 1090.37047) Full Text: DOI
Le Calvez, Patrice Unlinked invariant sets of diffeomorphisms of the torus and the annulus. (Ensembles invariants non enlacés des difféomorphismes du tore et de l’anneau.) (French. English summary) Zbl 1056.37056 Invent. Math. 155, No. 3, 561-603 (2004). MSC: 37E30 37E45 37J10 PDF BibTeX XML Cite \textit{P. Le Calvez}, Invent. Math. 155, No. 3, 561--603 (2004; Zbl 1056.37056) Full Text: DOI
Paternain, Gabriel P.; Polterovich, Leonid; Siburg, Karl Friedrich Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory. (English) Zbl 1048.53058 Mosc. Math. J. 3, No. 2, 593-619 (2003). Reviewer: Jan Chrastina (Brno) MSC: 53D12 57R17 PDF BibTeX XML Cite \textit{G. P. Paternain} et al., Mosc. Math. J. 3, No. 2, 593--619 (2003; Zbl 1048.53058) Full Text: arXiv
Mather, John N. Total disconnectedness of the quotient Aubry set in low dimensions. (English) Zbl 1046.37039 Commun. Pure Appl. Math. 56, No. 8, 1178-1183 (2003). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37J50 PDF BibTeX XML Cite \textit{J. N. Mather}, Commun. Pure Appl. Math. 56, No. 8, 1178--1183 (2003; Zbl 1046.37039) Full Text: DOI
Crovisier, Sylvain Ensembles de torsion nulle des applications déviant la verticale. (Twist-free sets of twist maps). (French) Zbl 1062.37032 Bull. Soc. Math. Fr. 131, No. 1, 23-39 (2003). Reviewer: Christophe Golé [MR 1975804] MSC: 37E40 37E45 37E30 PDF BibTeX XML Cite \textit{S. Crovisier}, Bull. Soc. Math. Fr. 131, No. 1, 23--39 (2003; Zbl 1062.37032) Full Text: DOI Link
Barles, Guy; Roquejoffre, Jean-Michel Large time behaviour of fronts governed by eikonal equations. (English) Zbl 1038.35173 Interfaces Free Bound. 5, No. 1, 83-102 (2003). MSC: 35R35 80A25 35B40 35F25 35J50 PDF BibTeX XML Cite \textit{G. Barles} and \textit{J.-M. Roquejoffre}, Interfaces Free Bound. 5, No. 1, 83--102 (2003; Zbl 1038.35173) Full Text: DOI
Fathi, Albert Heteroclinic orbits and Peierls set. (Orbites hétéroclines et ensemble de Peierls.) (French) Zbl 0915.58033 C. R. Acad. Sci., Paris, Sér. I, Math. 326, No. 10, 1213-1216 (1998). MSC: 37J99 PDF BibTeX XML Cite \textit{A. Fathi}, C. R. Acad. Sci., Paris, Sér. I, Math. 326, No. 10, 1213--1216 (1998; Zbl 0915.58033) Full Text: DOI
Forni, Giovanni Construction of invariant measures supported within the gaps of Aubry-Mather sets. (English) Zbl 0856.58024 Ergodic Theory Dyn. Syst. 16, No. 1, 51-86 (1996). Reviewer: V.A.Kaimanovich (Rennes) MSC: 37A25 37E40 PDF BibTeX XML Cite \textit{G. Forni}, Ergodic Theory Dyn. Syst. 16, No. 1, 51--86 (1996; Zbl 0856.58024) Full Text: DOI
Boyland, Philip The rotation set as a dynamical invariant. (English) Zbl 0764.58015 Twist mappings and their applications, Proc. Workshop, Minneapolis/MN (USA) 1989/90, IMA Vol. Math. Appl. 44, 73-86 (1992). Reviewer: R.Cowen (Gaborone) MSC: 37B99 PDF BibTeX XML Cite \textit{P. Boyland}, IMA Vol. Math. Appl. 44, 73--86 (1992; Zbl 0764.58015)
Le Calvez, Patrice Dynamical properties of diffeomorphisms of the annulus and the torus. (Propriétés dynamiques des difféomorphismes de l’anneau et du tore.) (French) Zbl 0784.58033 Astérisque. 204. Paris: Société Mathématique de France, 131 p. (1991). Reviewer: H.Kriete (Aachen) MSC: 37B99 37C70 54H20 39B12 PDF BibTeX XML Cite \textit{P. Le Calvez}, Propriétés dynamiques des difféomorphismes de l'anneau et du tore. Paris: Société Mathématique de France (1991; Zbl 0784.58033)
Veerman, J. J. P.; Tangerman, F. M. On Aubry-Mather sets. (English) Zbl 0718.58040 Physica D 46, No. 2, 149-162 (1990). Reviewer: Y.Kozai (Tokyo) MSC: 37D99 PDF BibTeX XML Cite \textit{J. J. P. Veerman} and \textit{F. M. Tangerman}, Physica D 46, No. 2, 149--162 (1990; Zbl 0718.58040) Full Text: DOI
Le Calvez, Patrice Aubry-Mather sets of a conservative diffeomorphism of the annulus are in general hyperbolic. (Les ensembles d’Aubry-Mather d’un difféomorphisme conservatif de l’anneau déviant la verticale sont en général hyperbolique.) (French) Zbl 0639.58005 C. R. Acad. Sci., Paris, Sér. I 306, No. 1, 51-54 (1988). Reviewer: D.Andrica MSC: 37E40 37E45 37D99 PDF BibTeX XML Cite \textit{P. Le Calvez}, C. R. Acad. Sci., Paris, Sér. I 306, No. 1, 51--54 (1988; Zbl 0639.58005)
Bellissard, J.; Lima, R.; Testard, D. A metal-insulator transition for the almost Mathieu model. (English) Zbl 0542.35059 Commun. Math. Phys. 88, 207-234 (1983). Reviewer: M.Thompson MSC: 35P25 35Q99 47A40 PDF BibTeX XML Cite \textit{J. Bellissard} et al., Commun. Math. Phys. 88, 207--234 (1983; Zbl 0542.35059) Full Text: DOI