Wilkinson, Mark Weyl Group Representation of Billiard Trajectories for One-dimensional Hard Sphere Dynamics. arXiv:2311.00446 Preprint, arXiv:2311.00446 [math-ph] (2023). MSC: 82C23 70Fxx 37A15 37C83 28C10 BibTeX Cite \textit{M. Wilkinson}, ``Weyl Group Representation of Billiard Trajectories for One-dimensional Hard Sphere Dynamics'', Preprint, arXiv:2311.00446 [math-ph] (2023) Full Text: arXiv OA License
Wilkinson, Mark Maximal Codimension Collisions and Invariant Measures for Hard Spheres on a Line. arXiv:2309.05815 Preprint, arXiv:2309.05815 [math.DS] (2023). MSC: 37C83 28C10 37A60 70G55 BibTeX Cite \textit{M. Wilkinson}, ``Maximal Codimension Collisions and Invariant Measures for Hard Spheres on a Line'', Preprint, arXiv:2309.05815 [math.DS] (2023) Full Text: arXiv OA License
Keating, Jonathan P.; Ueberschär, Henrik Multifractal eigenfunctions for a singular quantum billiard. (English) Zbl 1484.81046 Commun. Math. Phys. 389, No. 1, 543-569 (2022). MSC: 81Q50 37C83 81Q80 28A80 35P20 94A17 11E45 PDFBibTeX XMLCite \textit{J. P. Keating} and \textit{H. Ueberschär}, Commun. Math. Phys. 389, No. 1, 543--569 (2022; Zbl 1484.81046) Full Text: DOI arXiv
Żolądek, Henryk The Poncelet theorems in interpretation of Rafał Kołodziej. (English) Zbl 1401.37007 Kielanowski, Piotr (ed.) et al., Geometric methods in physics XXXV. Workshop and summer school, Białowieża, Poland, June 26 – July 2, 2016. Cham: Birkhäuser (ISBN 978-3-319-63593-4/hbk; 978-3-319-63594-1/ebook). Trends in Mathematics, 135-150 (2018). MSC: 37A05 37E10 14H52 37D50 28D05 28D10 PDFBibTeX XMLCite \textit{H. Żolądek}, in: Geometric methods in physics XXXV. Workshop and summer school, Białowieża, Poland, June 26 -- July 2, 2016. Cham: Birkhäuser. 135--150 (2018; Zbl 1401.37007) Full Text: DOI
Marco, Jean-Pierre Entropy of billiard maps and a dynamical version of the Birkhoff conjecture. (English) Zbl 1388.37043 J. Geom. Phys. 124, 413-420 (2018). Reviewer: George Stoica (Saint John) MSC: 37D50 37J35 28D20 PDFBibTeX XMLCite \textit{J.-P. Marco}, J. Geom. Phys. 124, 413--420 (2018; Zbl 1388.37043) Full Text: DOI
Squillace, Joseph Estimating the fractal dimension of sets determined by nonergodic parameters. (English) Zbl 1380.37077 Discrete Contin. Dyn. Syst. 37, No. 11, 5843-5859 (2017). MSC: 37D50 37C45 37A45 28A80 PDFBibTeX XMLCite \textit{J. Squillace}, Discrete Contin. Dyn. Syst. 37, No. 11, 5843--5859 (2017; Zbl 1380.37077) Full Text: DOI
Lapidus, Michel L.; Miller, Robyn L.; Niemeyer, Robert G. Nontrivial paths and periodic orbits of the \(T\)-fractal billiard table. (English) Zbl 1375.37115 Nonlinearity 29, No. 7, 2145-2172 (2016). Reviewer: Jacques Franchi (Strasbourg) MSC: 37D50 28A80 37D40 37C27 PDFBibTeX XMLCite \textit{M. L. Lapidus} et al., Nonlinearity 29, No. 7, 2145--2172 (2016; Zbl 1375.37115) Full Text: DOI arXiv
Kempton, Tom; Persson, Tomas Bernoulli convolutions and 1D dynamics. (English) Zbl 1357.37066 Nonlinearity 28, No. 11, 3921-3934 (2015). MSC: 37E05 37D50 28A80 PDFBibTeX XMLCite \textit{T. Kempton} and \textit{T. Persson}, Nonlinearity 28, No. 11, 3921--3934 (2015; Zbl 1357.37066) Full Text: DOI arXiv Link
Chen, Joe P.; Niemeyer, Robert G. Periodic billiard orbits of self-similar Sierpiński carpets. (English) Zbl 1371.37069 J. Math. Anal. Appl. 416, No. 2, 969-994 (2014). MSC: 37D50 28A80 PDFBibTeX XMLCite \textit{J. P. Chen} and \textit{R. G. Niemeyer}, J. Math. Anal. Appl. 416, No. 2, 969--994 (2014; Zbl 1371.37069) Full Text: DOI arXiv
Dragović, Vladimir; Radnović, Milena Pseudo-integrable billiards and arithmetic dynamics. (English) Zbl 1351.37160 J. Mod. Dyn. 8, No. 1, 109-132 (2014). MSC: 37D50 37J35 37A05 28D05 PDFBibTeX XMLCite \textit{V. Dragović} and \textit{M. Radnović}, J. Mod. Dyn. 8, No. 1, 109--132 (2014; Zbl 1351.37160) Full Text: DOI arXiv
Niemeyer, Robert G. Properties of the flow on a polygonal Andreev billiard. arXiv:1411.1825 Preprint, arXiv:1411.1825 [math.DS] (2014). MSC: 28A80 37D40 37D50 28A75 37C27 37E35 37F40 58J99 BibTeX Cite \textit{R. G. Niemeyer}, ``Properties of the flow on a polygonal Andreev billiard'', Preprint, arXiv:1411.1825 [math.DS] (2014) Full Text: arXiv OA License
Lapidus, Michel L.; Niemeyer, Robert G. The current state of fractal billiards. (English) Zbl 1321.37028 Carfì, David (ed.) et al., Fractal geometry and dynamical systems in pure and applied mathematics II: Fractals in applied mathematics. Selected papers based on three conferences following the passing of Benoît Mandelbrot in October 2010. 1st PISRS 2011 international conference on analysis, fractal geometry, dynamical systems and economics, Messina, Italy, November 8–12, 2011, AMS special session on fractal geometry in pure and applied mathematics, in memory of Benoît Mandelbrot, Boston, MA, USA, January 2012, AMS special session on geometry and analysis on fractal spaces, Honolulu, HI, USA, March 2012. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-9148-3/pbk; 978-1-4704-1083-4/ebook). Contemporary Mathematics 601, 251-288 (2013). MSC: 37D40 28A80 37D50 28A75 37C27 37E35 37F40 53D25 PDFBibTeX XMLCite \textit{M. L. Lapidus} and \textit{R. G. Niemeyer}, Contemp. Math. 601, 251--288 (2013; Zbl 1321.37028) Full Text: DOI arXiv
Lapidus, Michel L.; Niemeyer, Robert G. Sequences of compatible periodic hybrid orbits of prefractal Koch snowflake billiards. (English) Zbl 1364.28008 Discrete Contin. Dyn. Syst. 33, No. 8, 3719-3740 (2013). MSC: 28A80 37D40 37D50 PDFBibTeX XMLCite \textit{M. L. Lapidus} and \textit{R. G. Niemeyer}, Discrete Contin. Dyn. Syst. 33, No. 8, 3719--3740 (2013; Zbl 1364.28008) Full Text: DOI arXiv
Arroyo, Aubin; Markarian, Roberto; Sanders, David P. Structure and evolution of strange attractors in non-elastic triangular billiards. (English) Zbl 1331.37036 Chaos 22, No. 2, 026107, 12 p. (2012). MSC: 37D45 37D50 37D05 37B35 28A80 PDFBibTeX XMLCite \textit{A. Arroyo} et al., Chaos 22, No. 2, 026107, 12 p. (2012; Zbl 1331.37036) Full Text: DOI arXiv
Merenkov, Sergei; Zharnitsky, Vadim Hausdorff dimension of three-period orbits in Birkhoff billiards. (English) Zbl 1250.37017 Nonlinearity 25, No. 7, 1947-1954 (2012). MSC: 37C45 37D50 28A78 37J45 PDFBibTeX XMLCite \textit{S. Merenkov} and \textit{V. Zharnitsky}, Nonlinearity 25, No. 7, 1947--1954 (2012; Zbl 1250.37017) Full Text: DOI arXiv Link
Kuetche, Victor K.; Bouetou, Thomas B.; Kofane, Timoleon C. Fractal structure of ferromagnets: The singularity structure analysis. (English) Zbl 1272.82037 J. Math. Phys. 52, No. 9, 092903, 23 p. (2011). MSC: 82D40 28A80 35Q53 35Q51 35C08 35L67 37K10 37D50 37K35 PDFBibTeX XMLCite \textit{V. K. Kuetche} et al., J. Math. Phys. 52, No. 9, 092903, 23 p. (2011; Zbl 1272.82037) Full Text: DOI
Cheung, Yitwah; Hubert, Pascal; Masur, Howard Dichotomy for the Hausdorff dimension of the set of nonergodic directions. (English) Zbl 1220.37039 Invent. Math. 183, No. 2, 337-383 (2011). Reviewer: Bernd O. Stratmann (Bremen) MSC: 37A25 37D50 37F35 28A78 11K55 PDFBibTeX XMLCite \textit{Y. Cheung} et al., Invent. Math. 183, No. 2, 337--383 (2011; Zbl 1220.37039) Full Text: DOI arXiv
Fré, Pietro; Sorin, Alexander S. Supergravity black holes and billiards and the Liouville integrable structure associated with Borel algebras. (English) Zbl 1271.83080 J. High Energy Phys. 2010, No. 3, Paper No. 066, 53 p. (2010). MSC: 83E50 83C57 81T30 37D50 37J35 28A05 PDFBibTeX XMLCite \textit{P. Fré} and \textit{A. S. Sorin}, J. High Energy Phys. 2010, No. 3, Paper No. 066, 53 p. (2010; Zbl 1271.83080) Full Text: DOI arXiv
Hofbauer, F. Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations. (English) Zbl 1212.37064 Commentat. Math. Univ. Carol. 50, No. 2, 221-243 (2009). MSC: 37D50 28A78 37C45 37A35 PDFBibTeX XMLCite \textit{F. Hofbauer}, Commentat. Math. Univ. Carol. 50, No. 2, 221--243 (2009; Zbl 1212.37064) Full Text: EuDML EMIS
Courbage, Maurice Note on spectral theory, mixing and transport. (English) Zbl 1136.37308 Collet, P. (ed.) et al., Chaotic dynamics and transport in classical and quantum systems. Proceedings of the NATO Advanced Study Institute and international summer school, Cargèse, Corsica, France, 18–30 August, 2003. Dordrecht: Springer (ISBN 1-4020-2946-2/pbk; 1-4020-2945-4/hbk; 1-4020-2947-0/e-book). NATO Science Series II: Mathematics, Physics and Chemistry 182, 15-33 (2005). MSC: 37A30 28D05 37A25 37A60 37D50 60G50 60J60 PDFBibTeX XMLCite \textit{M. Courbage}, NATO Sci. Ser. II, Math. Phys. Chem. 182, 15--33 (2005; Zbl 1136.37308)
Kahng, Byungik The invariant fractals of symplectic piecewise affine elliptic dynamics. (English) Zbl 1081.37026 Lapidus, Michel L. (ed.) et al., Fractal geometry and applications: A jubilee of Benoît Mandelbrot. Analysis, number theory, and dynamical systems. In part the proceedings of a special session held during the annual meeting of the American Mathematical Society, San Diego, CA, USA, January 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3637-4/v.1; 0-8218-3292-1/set). Proceedings of Symposia in Pure Mathematics 72, Pt. 1, 375-389 (2004). Reviewer: Grzegorz Swiatek (University Park) MSC: 37E99 28A80 37J10 37N20 28A78 37D50 94A15 94A12 37C45 PDFBibTeX XMLCite \textit{B. Kahng}, Proc. Symp. Pure Math. 72, 375--389 (2004; Zbl 1081.37026)
Szász, Domokos; Varjú, Tamás Local limit theorem for the Lorentz process and its recurrence in the plane. (English) Zbl 1115.37009 Ergodic Theory Dyn. Syst. 24, No. 1, 257-278 (2004). Reviewer: Olaf Ninnemann (Berlin) MSC: 37A60 28D05 37D50 PDFBibTeX XMLCite \textit{D. Szász} and \textit{T. Varjú}, Ergodic Theory Dyn. Syst. 24, No. 1, 257--278 (2004; Zbl 1115.37009) Full Text: DOI arXiv
Kenny, Robert Estimates of Hausdorff dimension for the non-wandering set of an open planar billiard. (English) Zbl 1049.37023 Can. J. Math. 56, No. 1, 115-133 (2004). MSC: 37D50 37C45 28A78 PDFBibTeX XMLCite \textit{R. Kenny}, Can. J. Math. 56, No. 1, 115--133 (2004; Zbl 1049.37023) Full Text: DOI
Ree, Suhan Fractal analysis on a classical hard-wall billiard with openings using a two-dimensional set of initial conditions. (English) Zbl 1073.37519 Chaos Solitons Fractals 18, No. 4, 843-847 (2003). MSC: 37D50 37D45 28A80 PDFBibTeX XMLCite \textit{S. Ree}, Chaos Solitons Fractals 18, No. 4, 843--847 (2003; Zbl 1073.37519) Full Text: DOI arXiv
Cheung, Yitwah [Boshernitzan, Michael] Hausdorff dimension of the set of nonergodic directions (with an Appendix by M. Boshernitzan). (English) Zbl 1037.37018 Ann. Math. (2) 158, No. 2, 661-678 (2003). MSC: 37D50 11J70 28A80 37A05 11K55 82C05 PDFBibTeX XMLCite \textit{Y. Cheung}, Ann. Math. (2) 158, No. 2, 661--678 (2003; Zbl 1037.37018) Full Text: DOI arXiv Euclid
Masur, Howard; Tabachnikov, Serge Rational billiards and flat structures. (English) Zbl 1057.37034 Hasselblatt, B. (ed.) et al., Handbook of dynamical systems. Volume 1A. Amsterdam: North-Holland (ISBN 0-444-82669-6/hbk). 1015-1089 (2002). Reviewer: Mike Hurley (Cleveland) MSC: 37D50 37-02 37A25 37F99 28D05 30F60 PDFBibTeX XMLCite \textit{H. Masur} and \textit{S. Tabachnikov}, in: Handbook of dynamical systems. Volume 1A. Amsterdam: North-Holland. 1015--1089 (2002; Zbl 1057.37034)
Halbeisen, Lorenz; Hungerbühler, Norbert On periodic billiard trajectories in obtuse triangles. (English) Zbl 0970.37028 SIAM Rev. 42, No. 4, 657-670 (2000). Reviewer: C.Mira (Quint) MSC: 37D50 28D10 37E99 PDFBibTeX XMLCite \textit{L. Halbeisen} and \textit{N. Hungerbühler}, SIAM Rev. 42, No. 4, 657--670 (2000; Zbl 0970.37028) Full Text: DOI
Chernov, N. Decay of correlations and dispersing billiards. (English) Zbl 1047.37503 J. Stat. Phys. 94, No. 3-4, 513-556 (1999). MSC: 37D50 28D05 37A99 37C40 82C40 PDFBibTeX XMLCite \textit{N. Chernov}, J. Stat. Phys. 94, No. 3--4, 513--556 (1999; Zbl 1047.37503)
Simányi, Nándor Ergodicity of hard spheres in a box. (English) Zbl 0959.37007 Ergodic Theory Dyn. Syst. 19, No. 3, 741-766 (1999). Reviewer: Jialin Hong (Beijing) MSC: 37A25 28D05 37A60 37D50 PDFBibTeX XMLCite \textit{N. Simányi}, Ergodic Theory Dyn. Syst. 19, No. 3, 741--766 (1999; Zbl 0959.37007) Full Text: DOI arXiv Link
Vorobets, Ya. B. Ergodicity of billiards in polygons. (English. Russian original) Zbl 0886.58065 Sb. Math. 188, No. 3, 389-434 (1997); translation from Mat. Sb. 188, No. 3, 65-112 (1997). MSC: 37A25 28D10 37D50 PDFBibTeX XMLCite \textit{Ya. B. Vorobets}, Sb. Math. 188, No. 3, 389--434 (1997; Zbl 0886.58065); translation from Mat. Sb. 188, No. 3, 65--112 (1997) Full Text: DOI
Szász, D. Boltzmann’s ergodic hypothesis, a conjecture for centuries? (English) Zbl 0852.58060 Stud. Sci. Math. Hung. 31, No. 1-3, 299-322 (1996). Reviewer: H.Crauel (Saarbrücken) MSC: 37A99 01A60 58-03 28D99 37D99 82B03 PDFBibTeX XMLCite \textit{D. Szász}, Stud. Sci. Math. Hung. 31, No. 1--3, 299--322 (1996; Zbl 0852.58060)
Vorobets, Ya. B. Ergodicity of billiards in polygons: explicit examples. (English. Russian original) Zbl 1055.37500 Russ. Math. Surv. 51, No. 4, 756-757 (1996); translation from Usp. Mat. Nauk 51, No. 4, 151-152 (1996). MSC: 37A25 28D10 37D50 PDFBibTeX XMLCite \textit{Ya. B. Vorobets}, Russ. Math. Surv. 51, No. 4, 756--757 (1996; Zbl 1055.37500); translation from Usp. Mat. Nauk 51, No. 4, 151--152 (1996) Full Text: DOI
Gal’perin, G. A.; Chernov, N. I. Billiards and chaos. With a preface by Ya. G. Sinaj. (Billiardy i khaos.) (Russian) Zbl 0790.58001 Novoe v Zhizni, Nauke, Tekhnike. Seriya Matematika, Kibernetika. 91-5. Moskva: Znanie. 48 p. (1991). MSC: 58-01 37D45 28Dxx 37A99 70K50 PDFBibTeX XMLCite \textit{G. A. Gal'perin} and \textit{N. I. Chernov}, Billiardy i khaos (Russian). Moskva: Znanie (1991; Zbl 0790.58001)
Sinaĭ, Ya. G.; Chernov, N. I. Ergodic properties of certain systems of two-dimensional discs and three- dimensional balls. (English. Russian original) Zbl 0644.58007 Russ. Math. Surv. 42, No. 3, 181-207 (1987); translation from Usp. Mat. Nauk 42, No. 3(255), 153-174 (1987). Reviewer: I. U. Bronshteĭn MSC: 37A99 28D10 18D20 PDFBibTeX XMLCite \textit{Ya. G. Sinaĭ} and \textit{N. I. Chernov}, Russ. Math. Surv. 42, No. 3, 181--207 (1987; Zbl 0644.58007); translation from Usp. Mat. Nauk 42, No. 3(255), 153--174 (1987) Full Text: DOI
Gutkin, Eugene Billiards in polygons. (English) Zbl 0593.58016 Physica D 19, 311-333 (1986). Reviewer: M.Denker MSC: 37A99 28D10 54H20 PDFBibTeX XMLCite \textit{E. Gutkin}, Physica D 19, 311--333 (1986; Zbl 0593.58016) Full Text: DOI
Boshernitzan, Michael A condition for minimal interval exchange maps to be uniquely ergodic. (English) Zbl 0602.28009 Duke Math. J. 52, 723-752 (1985). Reviewer: Jaromir Šiška (Praha) MSC: 37A25 37D50 37E05 28D15 28D10 PDFBibTeX XMLCite \textit{M. Boshernitzan}, Duke Math. J. 52, 723--752 (1985; Zbl 0602.28009) Full Text: DOI
Kołodziej, Rafał The rotation number of some transformation related to the billiards on an elliptic table. (English) Zbl 0589.28011 Stud. Math. 81, 293-302 (1985). MSC: 28D05 28D10 PDFBibTeX XMLCite \textit{R. Kołodziej}, Stud. Math. 81, 293--302 (1985; Zbl 0589.28011) Full Text: DOI
Chernov, N. I. Structure of transversal leaves in multidimensional semidispersing billiards. (English. Russian original) Zbl 0552.28015 Funct. Anal. Appl. 16, 270-280 (1983); translation from Funkts. Anal. Prilozh. 16, No. 4, 35-46 (1982). Reviewer: B.Riečan MSC: 28D05 PDFBibTeX XMLCite \textit{N. I. Chernov}, Funct. Anal. Appl. 16, 270--280 (1983; Zbl 0552.28015); translation from Funkts. Anal. Prilozh. 16, No. 4, 35--46 (1982) Full Text: DOI
Cornfeld, I. P.; Fomin, S. V.; Sinai, Ya. G. Ergodic theory. Transl. from the Russian by A. B. Sossinskii. (English) Zbl 0493.28007 Grundlehren der Mathematischen Wissenschaften, 245. New York-Heidelberg-Berlin: Springer-Verlag. X, 486 p. DM 118.00; $ 52.40 (1982). MSC: 28Dxx 28-02 37A99 11A55 60G10 82B05 PDFBibTeX XML
Kornfel’d, I. P.; Sinaj, Ya. G.; Fomin, S. V. Ergodic theory. (Ehrgodicheskaya teoriya). (Russian) Zbl 0508.28008 Moskva: “Nauka”. 384 p. R. 2.80 (1980). MSC: 28Dxx 28-01 PDFBibTeX XML
Sinai, Ya. G. Ergodic properties of Lorentz gas. (Russian) Zbl 0414.28015 Funkts. Anal. Prilozh. 13, No. 3, 46-59 (1979). MSC: 37D99 37A60 28D05 82D05 PDFBibTeX XMLCite \textit{Ya. G. Sinai}, Funkts. Anal. Prilozh. 13, No. 3, 46--59 (1979; Zbl 0414.28015)
Sinai, Ya. G. Billiard trajectories in a polyhedral angle. (English) Zbl 0426.28019 Russ. Math. Surv. 33, No. 1, 219-220 (1978). MSC: 37D50 28D99 PDFBibTeX XMLCite \textit{Ya. G. Sinai}, Russ. Math. Surv. 33, No. 1, 219--220 (1978; Zbl 0426.28019) Full Text: DOI
Sinai, Ya. G. Billiard trajectories in a polyhedral angle. (Russian) Zbl 0415.28021 Usp. Mat. Nauk 33, No. 1(199), 229-230 (1978). MSC: 37D50 28D99 PDFBibTeX XMLCite \textit{Ya. G. Sinai}, Usp. Mat. Nauk 33, No. 1(199), 229--230 (1978; Zbl 0415.28021)