Guzzo, Massimiliano; Lega, Elena Theory and applications of fast Lyapunov indicators to model problems of celestial mechanics. (English) Zbl 07725899 Celest. Mech. Dyn. Astron. 135, No. 4, Paper No. 37, 36 p. (2023). MSC: 70F15 70K55 PDFBibTeX XMLCite \textit{M. Guzzo} and \textit{E. Lega}, Celest. Mech. Dyn. Astron. 135, No. 4, Paper No. 37, 36 p. (2023; Zbl 07725899) Full Text: DOI
Paez, Rocío I.; Guzzo, Massimiliano On the semi-analytical construction of halo orbits and halo tubes in the elliptic restricted three-body problem. (English) Zbl 1502.70022 Physica D 439, Article ID 133402, 14 p. (2022). MSC: 70F07 85A99 PDFBibTeX XMLCite \textit{R. I. Paez} and \textit{M. Guzzo}, Physica D 439, Article ID 133402, 14 p. (2022; Zbl 1502.70022) Full Text: DOI arXiv
Cardin, Franco; Guzzo, Massimiliano Integrability of close encounters in the spatial restricted three-body problem. (English) Zbl 1505.70031 Commun. Contemp. Math. 24, No. 6, Article ID 2150040, 41 p. (2022). MSC: 70F07 70F16 70H20 PDFBibTeX XMLCite \textit{F. Cardin} and \textit{M. Guzzo}, Commun. Contemp. Math. 24, No. 6, Article ID 2150040, 41 p. (2022; Zbl 1505.70031) Full Text: DOI arXiv
Paez, Rocío I.; Guzzo, Massimiliano Transits close to the Lagrangian solutions \(L_1, L_2\) in the elliptic restricted three-body problem. (English) Zbl 1476.70026 Nonlinearity 34, No. 9, 6417-6449 (2021). MSC: 70F07 70F15 37J40 70M20 37D10 37D05 PDFBibTeX XMLCite \textit{R. I. Paez} and \textit{M. Guzzo}, Nonlinearity 34, No. 9, 6417--6449 (2021; Zbl 1476.70026) Full Text: DOI arXiv
Guzzo, Massimiliano; Efthymiopoulos, Christos; Paez, Rocío I. Semi-analytic computations of the speed of Arnold diffusion along single resonances in a priori stable Hamiltonian systems. (English) Zbl 1443.37047 J. Nonlinear Sci. 30, No. 3, 851-901 (2020). Reviewer: Xiang Zhang (Shanghai) MSC: 37J40 37J25 37J35 70H08 70H09 PDFBibTeX XMLCite \textit{M. Guzzo} et al., J. Nonlinear Sci. 30, No. 3, 851--901 (2020; Zbl 1443.37047) Full Text: DOI arXiv
Cardin, Franco; Guzzo, Massimiliano Integrability of the spatial restricted three-body problem near collisions (an announcement). (English) Zbl 1461.70015 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 30, No. 1, 195-204 (2019). Reviewer: Maria Gousidou-Koutita (Thessaloniki) MSC: 70F07 70F16 70H20 PDFBibTeX XMLCite \textit{F. Cardin} and \textit{M. Guzzo}, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 30, No. 1, 195--204 (2019; Zbl 1461.70015) Full Text: DOI
Guzzo, Massimiliano; Lega, Elena Geometric chaos indicators and computations of the spherical hypertube manifolds of the spatial circular restricted three-body problem. (English) Zbl 1392.70004 Physica D 373, 38-58 (2018). MSC: 70F07 70K55 34C28 34C45 PDFBibTeX XMLCite \textit{M. Guzzo} and \textit{E. Lega}, Physica D 373, 38--58 (2018; Zbl 1392.70004) Full Text: DOI HAL
Guzzo, Massimiliano; Lega, Elena The Nekhoroshev theorem and the observation of long-term diffusion in Hamiltonian systems. (English) Zbl 1369.70036 Regul. Chaotic Dyn. 21, No. 6, 707-719 (2016). MSC: 70H08 37J40 PDFBibTeX XMLCite \textit{M. Guzzo} and \textit{E. Lega}, Regul. Chaotic Dyn. 21, No. 6, 707--719 (2016; Zbl 1369.70036) Full Text: DOI
Lega, Elena; Guzzo, Massimiliano Three-dimensional representations of the tube manifolds of the planar restricted three-body problem. (English) Zbl 1364.65284 Physica D 325, 41-52 (2016). MSC: 65P99 70F07 70K20 37D05 PDFBibTeX XMLCite \textit{E. Lega} and \textit{M. Guzzo}, Physica D 325, 41--52 (2016; Zbl 1364.65284) Full Text: DOI
Guzzo, M.; Chierchia, L.; Benettin, G. The steep Nekhoroshev’s theorem. (English) Zbl 1337.37038 Commun. Math. Phys. 342, No. 2, 569-601 (2016). Reviewer: William J. Satzer jun. (St. Paul) MSC: 37J25 37J40 70F15 70E50 70H05 PDFBibTeX XMLCite \textit{M. Guzzo} et al., Commun. Math. Phys. 342, No. 2, 569--601 (2016; Zbl 1337.37038) Full Text: DOI
Schirinzi, Gabriella; Guzzo, Massimiliano Numerical verification of the steepness of three and four degrees of freedom Hamiltonian systems. (English) Zbl 1372.70040 Regul. Chaotic Dyn. 20, No. 1, 1-18 (2015). MSC: 70F15 70H08 37J40 PDFBibTeX XMLCite \textit{G. Schirinzi} and \textit{M. Guzzo}, Regul. Chaotic Dyn. 20, No. 1, 1--18 (2015; Zbl 1372.70040) Full Text: DOI
Guzzo, Massimiliano; Lega, Elena Evolution of the tangent vectors and localization of the stable and unstable manifolds of hyperbolic orbits by fast Lyapunov indicators. (English) Zbl 1351.37106 SIAM J. Appl. Math. 74, No. 4, 1058-1086 (2014). MSC: 37D10 37D25 70F07 PDFBibTeX XMLCite \textit{M. Guzzo} and \textit{E. Lega}, SIAM J. Appl. Math. 74, No. 4, 1058--1086 (2014; Zbl 1351.37106) Full Text: DOI arXiv
Guzzo, Massimiliano; Chierchia, Luigi; Benettin, Giancarlo The steep Nekhoroshev’s theorem and optimal stability exponents (an announcement). (English) Zbl 1326.37040 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 25, No. 3, 293-299 (2014). MSC: 37J40 34D20 70H08 PDFBibTeX XMLCite \textit{M. Guzzo} et al., Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 25, No. 3, 293--299 (2014; Zbl 1326.37040) Full Text: DOI arXiv
Schirinzi, Gabriella; Guzzo, Massimiliano On the formulation of new explicit conditions for steepness from a former result of N.N. Nekhoroshev. (English) Zbl 1302.58002 J. Math. Phys. 54, No. 7, 072702, 22 p. (2013). MSC: 58A20 37N05 70H05 37J35 37J25 PDFBibTeX XMLCite \textit{G. Schirinzi} and \textit{M. Guzzo}, J. Math. Phys. 54, No. 7, 072702, 22 p. (2013; Zbl 1302.58002) Full Text: DOI
Bernardi, Olga; Cardin, Franco; Guzzo, Massimiliano New estimates for Evans’ variational approach to weak KAM theory. (English) Zbl 1277.35127 Commun. Contemp. Math. 15, No. 2, Paper No. 1250055, 36 p. (2013). Reviewer: Jiansheng Geng (Nanjing) MSC: 35F21 70H20 70H08 70H30 PDFBibTeX XMLCite \textit{O. Bernardi} et al., Commun. Contemp. Math. 15, No. 2, Paper No. 1250055, 36 p. (2013; Zbl 1277.35127) Full Text: DOI arXiv
Guzzo, Massimiliano; Lega, Elena; Froeschlé, Claude First numerical investigation of a conjecture by N. N. Nekhoroshev about stability in quasi-integrable systems. (English) Zbl 1317.37059 Chaos 21, No. 3, 033101, 12 p. (2011). MSC: 37J40 37J25 70H08 70H14 PDFBibTeX XMLCite \textit{M. Guzzo} et al., Chaos 21, No. 3, 033101, 12 p. (2011; Zbl 1317.37059) Full Text: DOI
Todorović, Nataša; Guzzo, Massimiliano; Lega, Elena; Froeschlé, Claude A numerical study of the stabilization effect of steepness. (English) Zbl 1270.70060 Celest. Mech. Dyn. Astron. 110, No. 4, 389-398 (2011). MSC: 70H14 70F05 70-08 65P10 PDFBibTeX XMLCite \textit{N. Todorović} et al., Celest. Mech. Dyn. Astron. 110, No. 4, 389--398 (2011; Zbl 1270.70060) Full Text: DOI
Lega, Elena; Guzzo, Massimiliano; Froeschlé, Claude A numerical study of the hyperbolic manifolds in a priori unstable systems. A comparison with Melnikov approximations. (English) Zbl 1291.70063 Celest. Mech. Dyn. Astron. 107, No. 1-2, 115-127 (2010). MSC: 70H14 70-08 PDFBibTeX XMLCite \textit{E. Lega} et al., Celest. Mech. Dyn. Astron. 107, No. 1--2, 115--127 (2010; Zbl 1291.70063) Full Text: DOI HAL
Lega, Elena; Guzzo, Massimiliano; Froeschlé, Claude A numerical study of the size of the homoclinic tangle of hyperbolic tori and its correlation with Arnold diffusion in Hamiltonian systems. (English) Zbl 1291.70062 Celest. Mech. Dyn. Astron. 107, No. 1-2, 129-144 (2010). MSC: 70H14 70-08 PDFBibTeX XMLCite \textit{E. Lega} et al., Celest. Mech. Dyn. Astron. 107, No. 1--2, 129--144 (2010; Zbl 1291.70062) Full Text: DOI HAL
Celletti, Alessandra; Guzzo, Massimiliano Cantori of the dissipative sawtooth map. (English) Zbl 1311.70029 Chaos 19, No. 1, 013139, 6 p. (2009). MSC: 70H08 PDFBibTeX XMLCite \textit{A. Celletti} and \textit{M. Guzzo}, Chaos 19, No. 1, 013139, 6 p. (2009; Zbl 1311.70029) Full Text: DOI
Guzzo, Massimiliano; Lega, Elena; Froeschlé, Claude A numerical study of Arnold diffusion in a priori unstable systems. (English) Zbl 1185.37143 Commun. Math. Phys. 290, No. 2, 557-576 (2009). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37J40 70H08 70-08 PDFBibTeX XMLCite \textit{M. Guzzo} et al., Commun. Math. Phys. 290, No. 2, 557--576 (2009; Zbl 1185.37143) Full Text: DOI
Lega, Elena; Guzzo, Massimiliano; Froeschlé, Claude Measure of the exponential splitting of the homoclinic tangle in four-dimensional symplectic mappings. (English) Zbl 1165.70022 Celest. Mech. Dyn. Astron. 104, No. 1-2, 191-204 (2009). MSC: 70H09 70H15 PDFBibTeX XMLCite \textit{E. Lega} et al., Celest. Mech. Dyn. Astron. 104, No. 1--2, 191--204 (2009; Zbl 1165.70022) Full Text: DOI
Namouni, F.; Guzzo, M.; Lega, E. On the integrability of stellar motion in an accelerated logarithmic potential. (English) Zbl 1156.85306 Astron. Astrophys. 489, No. 3, 1363-1367 (2008). MSC: 85A05 70F15 PDFBibTeX XMLCite \textit{F. Namouni} et al., Astron. Astrophys. 489, No. 3, 1363--1367 (2008; Zbl 1156.85306) Full Text: DOI arXiv
Benettin, Giancarlo; Guzzo, Massimiliano; Neishtadt, Anatoly A new problem of adiabatic invariance related to the rigid body dynamics. (English) Zbl 1342.70052 Discrete Contin. Dyn. Syst. 21, No. 3, 959-975 (2008). MSC: 70H11 70E20 37J40 PDFBibTeX XMLCite \textit{G. Benettin} et al., Discrete Contin. Dyn. Syst. 21, No. 3, 959--975 (2008; Zbl 1342.70052) Full Text: DOI
Benettin, Giancarlo; Guzzo, Massimiliano; Marini, Valerio Adiabatic chaos in the spin-orbit problem. (English) Zbl 1342.70034 Celest. Mech. Dyn. Astron. 101, No. 1-2, 203-224 (2008). MSC: 70F15 37D45 37N05 70K55 PDFBibTeX XMLCite \textit{G. Benettin} et al., Celest. Mech. Dyn. Astron. 101, No. 1--2, 203--224 (2008; Zbl 1342.70034) Full Text: DOI
Guzzo, Massimiliano An overview on the Nekhoroshev theorem. (English) Zbl 1157.85305 Benest, Daniel (ed.) et al., Topics in gravitational dynamics. Solar, extra-solar and galactic systems. Selected papers based on the presentations at the 2006 Aussois winter school, France. Berlin: Springer (ISBN 978-3-540-72983-9/hbk). Lecture Notes in Physics 729, 1-28 (2007). MSC: 85A05 37N20 70F15 PDFBibTeX XMLCite \textit{M. Guzzo}, Lect. Notes Phys. 729, 1--28 (2007; Zbl 1157.85305) Full Text: DOI
Namouni, F.; Guzzo, M. The accelerated Kepler problem. (English) Zbl 1162.70310 Celest. Mech. Dyn. Astron. 99, No. 1, 31-44 (2007). MSC: 70F05 PDFBibTeX XMLCite \textit{F. Namouni} and \textit{M. Guzzo}, Celest. Mech. Dyn. Astron. 99, No. 1, 31--44 (2007; Zbl 1162.70310) Full Text: DOI arXiv
Guzzo, Massimiliano Fourier analysis of chaotic motions and applications to celestial mechanics. (English) Zbl 1151.70007 Steves, B. A. (ed.) et al., Chaotic worlds: from order to disorder in gravitational \(N\)-body dynamical systems. Proceedings of the NATO Advanced Study Institute, Cortina, Italy, 8–20 September 2003. Dordrecht: Springer (ISBN 978-1-4020-4705-3/pbk; 1-4020-4704-5/hbk). NATO Science Series II: Mathematics, Physics and Chemistry 227, 167-200 (2006). MSC: 70H08 70F15 70-02 PDFBibTeX XMLCite \textit{M. Guzzo}, NATO Sci. Ser. II, Math. Phys. Chem. 227, 167--200 (2006; Zbl 1151.70007) Full Text: DOI
Benettin, G.; Fassò, F.; Guzzo, M. Long term stability of proper rotations and local chaotic motions in the perturbed Euler rigid body. (English) Zbl 1133.70310 Regul. Chaotic Dyn. 11, No. 1, 1-17 (2006). MSC: 70E20 37J40 70-08 70E17 70H08 PDFBibTeX XMLCite \textit{G. Benettin} et al., Regul. Chaotic Dyn. 11, No. 1, 1--17 (2006; Zbl 1133.70310) Full Text: DOI
Froeschlé, Claude; Lega, Elena; Guzzo, Massimiliano Analysis of the chaotic behaviour of orbits diffusing along the Arnold web. (English) Zbl 1185.37141 Celest. Mech. Dyn. Astron. 95, No. 1-4, 141-153 (2006). MSC: 37J40 70H09 70K43 PDFBibTeX XMLCite \textit{C. Froeschlé} et al., Celest. Mech. Dyn. Astron. 95, No. 1--4, 141--153 (2006; Zbl 1185.37141) Full Text: DOI
Guzzo, Massimiliano; Lega, Elena; Froeschlé, Claude Diffusion and stability in perturbed non-convex integrable systems. (English) Zbl 1100.37036 Nonlinearity 19, No. 5, 1049-1067 (2006). MSC: 37J40 37J25 70H08 PDFBibTeX XMLCite \textit{M. Guzzo} et al., Nonlinearity 19, No. 5, 1049--1067 (2006; Zbl 1100.37036) Full Text: DOI
Froeschlé, Claude; Guzzo, Massimiliano; Lega, Elena Local and global diffusion along resonant lines in discrete quasi-integrable dynamical systems. (English) Zbl 1083.37050 Celest. Mech. Dyn. Astron. 92, No. 1-3, 243-255 (2005). MSC: 37J40 70H08 PDFBibTeX XMLCite \textit{C. Froeschlé} et al., Celest. Mech. Dyn. Astron. 92, No. 1--3, 243--255 (2005; Zbl 1083.37050) Full Text: DOI
Guzzo, Massimiliano; Lega, Elena; Froeschlé, Claude First numerical evidence of global Arnold diffusion in quasi-integrable systems. (English) Zbl 1081.37035 Discrete Contin. Dyn. Syst., Ser. B 5, No. 3, 687-698 (2005). MSC: 37J40 70K43 PDFBibTeX XMLCite \textit{M. Guzzo} et al., Discrete Contin. Dyn. Syst., Ser. B 5, No. 3, 687--698 (2005; Zbl 1081.37035) Full Text: DOI arXiv
Benettin, Giancarlo; Fassò, Francesco; Guzzo, Massimiliano Long term stability of proper rotations of the perturbed Euler rigid body. (English) Zbl 1087.70003 Commun. Math. Phys. 250, No. 1, 133-160 (2004). MSC: 70E20 70E17 70E50 37J40 PDFBibTeX XMLCite \textit{G. Benettin} et al., Commun. Math. Phys. 250, No. 1, 133--160 (2004; Zbl 1087.70003) Full Text: DOI
Guzzo, Massimiliano A direct proof of the Nekhoroshev theorem for nearly integrable symplectic maps. (English) Zbl 1162.70321 Ann. Henri Poincaré 5, No. 6, 1013-1039 (2004). Reviewer: Giuseppe Gaeta (Milano) MSC: 70H09 37J40 70H08 PDFBibTeX XMLCite \textit{M. Guzzo}, Ann. Henri Poincaré 5, No. 6, 1013--1039 (2004; Zbl 1162.70321) Full Text: DOI
Guzzo, Massimiliano Long-term stability analysis of quasi-integrable degenerate systems through the spectral formulation of the Nekhoroshev theorem. (English) Zbl 1030.70009 Celest. Mech. Dyn. Astron. 83, No. 1-4, 303-323 (2002). Reviewer: Simos Ichtiaroglou (Thessaloniki) MSC: 70H08 37J40 70H14 37N05 70F15 PDFBibTeX XMLCite \textit{M. Guzzo}, Celest. Mech. Dyn. Astron. 83, No. 1--4, 303--323 (2002; Zbl 1030.70009) Full Text: DOI
Guzzo, Massimiliano; Knežević, Zoran; Milani, Andrea Probing the Nekhoroshev stability of asteroids. (English) Zbl 1045.70010 Celest. Mech. Dyn. Astron. 83, No. 1-4, 121-140 (2002). MSC: 70F15 70K20 37N05 PDFBibTeX XMLCite \textit{M. Guzzo} et al., Celest. Mech. Dyn. Astron. 83, No. 1--4, 121--140 (2002; Zbl 1045.70010) Full Text: DOI
Guzzo, Massimiliano; Lega, Elena; Froeschlé, Claude On the numerical detection of the effective stability of chaotic motions in quasi-integrable systems. (English) Zbl 0986.37076 Physica D 163, No. 1-2, 1-25 (2002). MSC: 37M25 65P10 70K20 PDFBibTeX XMLCite \textit{M. Guzzo} et al., Physica D 163, No. 1--2, 1--25 (2002; Zbl 0986.37076) Full Text: DOI
Guzzo, Massimiliano Improved leap-frog symplectic integrators for orbits of small eccentricity in the perturbed Kepler problem. (English) Zbl 1004.70004 Celest. Mech. Dyn. Astron. 80, No. 1, 63-80 (2001). MSC: 70-08 70F05 65P10 PDFBibTeX XMLCite \textit{M. Guzzo}, Celest. Mech. Dyn. Astron. 80, No. 1, 63--80 (2001; Zbl 1004.70004) Full Text: DOI
Guzzo, M. Nekhoroshev stability of quasi-integrable degenerate Hamiltonian systems. (English) Zbl 1012.37044 Regul. Chaotic Dyn. 4, No. 2, 78-102 (1999). MSC: 37J40 70H08 70F15 PDFBibTeX XMLCite \textit{M. Guzzo}, Regul. Chaotic Dyn. 4, No. 2, 78--102 (1999; Zbl 1012.37044) Full Text: DOI
Benettin, G.; Fassò, F.; Guzzo, M. Nekhoroshev-stability of \(L4\) and \(L5\) in the spatial restricted three-body problem. (English) Zbl 0934.70010 Regul. Chaotic Dyn. 3, No. 3, 56-72 (1998). Reviewer: Simos Ichtiaroglou (Thessaloniki) MSC: 70F07 70F15 70H14 37N05 PDFBibTeX XMLCite \textit{G. Benettin} et al., Regul. Chaotic Dyn. 3, No. 3, 56--72 (1998; Zbl 0934.70010) Full Text: DOI
Fassò, Francesco; Guzzo, Massimiliano; Benettin, Giancarlo Nekhoroshev-stability of elliptic equilibria of Hamiltonian systems. (English) Zbl 0928.37017 Commun. Math. Phys. 197, No. 2, 347-360 (1998). Reviewer: S.Zelik (Moskva) MSC: 37K45 37K05 70H05 PDFBibTeX XMLCite \textit{F. Fassò} et al., Commun. Math. Phys. 197, No. 2, 347--360 (1998; Zbl 0928.37017) Full Text: DOI
Benettin, Giancarlo; Fassò, Francesco; Guzzo, Massimiliano Fast rotations of the rigid body: A study by Hamiltonian perturbation theory. II: Gyroscopic rotations. (English) Zbl 0920.70009 Nonlinearity 10, No. 6, 1695-1717 (1997). MSC: 70E20 70E15 37J40 70E05 70H99 PDFBibTeX XMLCite \textit{G. Benettin} et al., Nonlinearity 10, No. 6, 1695--1717 (1997; Zbl 0920.70009) Full Text: DOI
Guzzo, Massimilliano; Morbidelli, Alessandro Construction of a Nekhoroshev like result for the asteroid belt dynamical system. (English) Zbl 0883.58032 Celest. Mech. Dyn. Astron. 66, No. 3, 255-292 (1997). MSC: 37N99 70F15 PDFBibTeX XMLCite \textit{M. Guzzo} and \textit{A. Morbidelli}, Celest. Mech. Dyn. Astron. 66, No. 3, 255--292 (1997; Zbl 0883.58032) Full Text: DOI
Morbidelli, Alessandro; Guzzo, Massimiliano The Nekhoroshev theorem and the asteroid belt dynamical system. (English) Zbl 0891.70007 Celest. Mech. Dyn. Astron. 65, No. 1-2, 107-136 (1997). Reviewer: M.Calvo (Zaragoza) MSC: 70F15 37J40 34D10 PDFBibTeX XMLCite \textit{A. Morbidelli} and \textit{M. Guzzo}, Celest. Mech. Dyn. Astron. 65, No. 1--2, 107--136 (1997; Zbl 0891.70007) Full Text: DOI