Weinreich, Max The dynamical degree of billiards in an algebraic curve. arXiv:2305.14287 Preprint, arXiv:2305.14287 [math.DS] (2023). MSC: 37C83 37P05 37F80 37B40 BibTeX Cite \textit{M. Weinreich}, ``The dynamical degree of billiards in an algebraic curve'', Preprint, arXiv:2305.14287 [math.DS] (2023) Full Text: arXiv OA License
Apisa, Paul; Saavedra, Rafael M.; Zhang, Christopher Periodic points on the regular and double \(n\)-gon surfaces. (English) Zbl 1504.32032 Geom. Dedicata 216, No. 6, Paper No. 69, 17 p. (2022). MSC: 32G15 37D40 14H15 PDFBibTeX XMLCite \textit{P. Apisa} et al., Geom. Dedicata 216, No. 6, Paper No. 69, 17 p. (2022; Zbl 1504.32032) Full Text: DOI arXiv
Friedland, Omer; Ueberschär, Henrik Superscarred quasimodes on flat surfaces with conical singularities. (English) Zbl 1487.35264 Stud. Math. 264, No. 3, 241-262 (2022). MSC: 35P20 35J25 37A25 37D45 PDFBibTeX XMLCite \textit{O. Friedland} and \textit{H. Ueberschär}, Stud. Math. 264, No. 3, 241--262 (2022; Zbl 1487.35264) Full Text: DOI arXiv
Larsen, Anne; Norton, Chaya; Zykoski, Bradley Strongly obtuse rational lattice triangles. (English) Zbl 1485.37033 Trans. Am. Math. Soc. 374, No. 10, 7119-7142 (2021). Reviewer: Thomas B. Ward (Newcastle) MSC: 37D40 37C83 37A30 37A44 11N25 52A10 PDFBibTeX XMLCite \textit{A. Larsen} et al., Trans. Am. Math. Soc. 374, No. 10, 7119--7142 (2021; Zbl 1485.37033) Full Text: DOI arXiv
Frączek, Krzysztof Ergodic properties of the ideal gas model for infinite billiards. (English) Zbl 1448.37003 Physica D 390, 9-14 (2019). MSC: 37A25 37B20 60G55 37C83 PDFBibTeX XMLCite \textit{K. Frączek}, Physica D 390, 9--14 (2019; Zbl 1448.37003) Full Text: DOI
Kaloshin, Vadim; Zhang, Ke Density of convex billiards with rational caustics. (English) Zbl 1400.37043 Nonlinearity 31, No. 11, 5214-5234 (2018). MSC: 37D50 37J40 37J50 70H08 PDFBibTeX XMLCite \textit{V. Kaloshin} and \textit{K. Zhang}, Nonlinearity 31, No. 11, 5214--5234 (2018; Zbl 1400.37043) Full Text: DOI arXiv
Garcia, Ronaldo A. Centers of inscribed circles in triangular orbits of an elliptic billiard. arXiv:1607.00179 Preprint, arXiv:1607.00179 [math.MG] (2016). MSC: 51M04 37D50 53A15 14H50 14E05 BibTeX Cite \textit{R. A. Garcia}, ``Centers of inscribed circles in triangular orbits of an elliptic billiard'', Preprint, arXiv:1607.00179 [math.MG] (2016) Full Text: arXiv OA License
Bedaride, Nicolas A characterization of quasi-rational polygons. (English) Zbl 1259.37029 Nonlinearity 25, No. 11, 3099-3110 (2012). MSC: 37E99 37D50 PDFBibTeX XMLCite \textit{N. Bedaride}, Nonlinearity 25, No. 11, 3099--3110 (2012; Zbl 1259.37029) Full Text: DOI arXiv
Marklof, Jens; Rudnick, Zeév Almost all eigenfunctions of a rational polygon are uniformly distributed. (English) Zbl 1242.37027 J. Spectr. Theory 2, No. 1, 107-113 (2012). MSC: 37D50 58J51 81Q50 PDFBibTeX XMLCite \textit{J. Marklof} and \textit{Z. Rudnick}, J. Spectr. Theory 2, No. 1, 107--113 (2012; Zbl 1242.37027) Full Text: DOI arXiv
Bobok, Jozef; Troubetzkoy, Serge Code and order in polygonal billiards. (English) Zbl 1259.37026 Topology Appl. 159, No. 1, 236-247 (2012). Reviewer: Hongkun Zhang (Amherst) MSC: 37D50 52A10 37C15 PDFBibTeX XMLCite \textit{J. Bobok} and \textit{S. Troubetzkoy}, Topology Appl. 159, No. 1, 236--247 (2012; Zbl 1259.37026) Full Text: DOI arXiv
Lapidus, Michel L.; Niemeyer, Robert G. Towards the Koch snowflake fractal billiard: computer experiments and mathematical conjectures. (English) Zbl 1222.37028 Amdeberhan, Tewodros (ed.) et al., Gems in experimental mathematics. AMS special session on experimental mathematics, Washington, DC, January 5, 2009. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4869-2/pbk). Contemporary Mathematics 517, 231-263 (2010). Reviewer: Anke Pohl (Zürich) MSC: 37D40 37D50 37C27 65D18 65P99 37A99 37C55 58A99 74H99 PDFBibTeX XMLCite \textit{M. L. Lapidus} and \textit{R. G. Niemeyer}, Contemp. Math. 517, 231--263 (2010; Zbl 1222.37028) Full Text: arXiv
Athreya, J. S.; Forni, G. Deviation of ergodic averages for rational polygonal billiards. (English) Zbl 1153.37001 Duke Math. J. 144, No. 2, 285-319 (2008). Reviewer: Akihiko Morimoto (Nagoya) MSC: 37A10 37D50 PDFBibTeX XMLCite \textit{J. S. Athreya} and \textit{G. Forni}, Duke Math. J. 144, No. 2, 285--319 (2008; Zbl 1153.37001) Full Text: DOI arXiv
McMullen, Curtis T. Foliations of Hilbert modular surfaces. (English) Zbl 1154.14020 Am. J. Math. 129, No. 1, 183-215 (2007). Reviewer: Xander Faber (Montreal) MSC: 14G35 37D50 37F10 PDFBibTeX XMLCite \textit{C. T. McMullen}, Am. J. Math. 129, No. 1, 183--215 (2007; Zbl 1154.14020) Full Text: DOI Link
Baryshnikov, Yuliy; Zharnitsky, Vadim Sub-Riemannian geometry and periodic orbits in classical billiards. (English) Zbl 1133.53023 Math. Res. Lett. 13, No. 4, 587-598 (2006). MSC: 53C17 37D50 PDFBibTeX XMLCite \textit{Y. Baryshnikov} and \textit{V. Zharnitsky}, Math. Res. Lett. 13, No. 4, 587--598 (2006; Zbl 1133.53023) Full Text: DOI
Bedford, Eric; Diller, Jeff Dynamics of a two parameter family of plane birational maps: maximal entropy. (English) Zbl 1116.37031 J. Geom. Anal. 16, No. 3, 409-430 (2006). Reviewer: Peter Raith (Wien) MSC: 37F10 14E05 37D50 37C40 37A35 PDFBibTeX XMLCite \textit{E. Bedford} and \textit{J. Diller}, J. Geom. Anal. 16, No. 3, 409--430 (2006; Zbl 1116.37031) Full Text: DOI arXiv
Eskin, Alex; Marklof, Jens; Witte Morris, Dave Unipotent flows on the space of branched covers of Veech surfaces. (English) Zbl 1085.37021 Ergodic Theory Dyn. Syst. 26, No. 1, 129-162 (2006). MSC: 37C85 37D50 PDFBibTeX XMLCite \textit{A. Eskin} et al., Ergodic Theory Dyn. Syst. 26, No. 1, 129--162 (2006; Zbl 1085.37021) Full Text: DOI arXiv
Baryshnikov, Y.; Zharnitsky, V. Billiards and nonholonomic distributions. (English. Russian original) Zbl 1120.37033 J. Math. Sci., New York 128, No. 2, 2706-2710 (2005); translation from Zap. Nauchn. Semin. POMI 300, 56-64 (2003). MSC: 37J10 37D50 37J60 70H05 PDFBibTeX XMLCite \textit{Y. Baryshnikov} and \textit{V. Zharnitsky}, J. Math. Sci., New York 128, No. 2, 2706--2710 (2005; Zbl 1120.37033); translation from Zap. Nauchn. Semin. POMI 300, 56--64 (2003) Full Text: DOI
Dogru, Filiz; Tabachnikov, Serge Dual billiards. (English) Zbl 1088.37014 Math. Intell. 27, No. 4, 18-25 (2005). Reviewer: Hans Crauel (Ilmenau) MSC: 37D50 30F10 70F15 PDFBibTeX XMLCite \textit{F. Dogru} and \textit{S. Tabachnikov}, Math. Intell. 27, No. 4, 18--25 (2005; Zbl 1088.37014) Full Text: DOI
Lochak, Pierre On arithmetic curves in the moduli spaces of curves. (English) Zbl 1094.14018 J. Inst. Math. Jussieu 4, No. 3, 443-508 (2005). Reviewer: Ernesto Girondo (Madrid) MSC: 14H30 32G15 14D22 PDFBibTeX XMLCite \textit{P. Lochak}, J. Inst. Math. Jussieu 4, No. 3, 443--508 (2005; Zbl 1094.14018) Full Text: DOI
Kleinbock, Dmitry; Weiss, Barak Bounded geodesics in moduli space. (English) Zbl 1075.37008 Int. Math. Res. Not. 2004, No. 30, 1551-1560 (2004). MSC: 37D40 53D25 37D50 PDFBibTeX XMLCite \textit{D. Kleinbock} and \textit{B. Weiss}, Int. Math. Res. Not. 2004, No. 30, 1551--1560 (2004; Zbl 1075.37008) Full Text: DOI arXiv
Monteil, Thierry A counter-example to the theorem of Hiemer and Snurnikov. (English) Zbl 1058.37040 J. Stat. Phys. 114, No. 5-6, 1619-1623 (2004). MSC: 37J10 37D50 70H05 PDFBibTeX XMLCite \textit{T. Monteil}, J. Stat. Phys. 114, No. 5--6, 1619--1623 (2004; Zbl 1058.37040) Full Text: DOI arXiv
Smillie, John; Weiss, Barak Minimal sets for flows on moduli space. (English) Zbl 1052.37025 Isr. J. Math. 142, 249-260 (2004). MSC: 37D40 37F10 37B05 57M50 PDFBibTeX XMLCite \textit{J. Smillie} and \textit{B. Weiss}, Isr. J. Math. 142, 249--260 (2004; Zbl 1052.37025) Full Text: DOI
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
Bedaride, N. Billiard complexity in rational polyhedra. (English) Zbl 1023.37024 Regul. Chaotic Dyn. 8, No. 1, 97-104 (2003). Reviewer: I.A.Taimanov (Novosibirsk) MSC: 37E30 37D50 37B10 PDFBibTeX XMLCite \textit{N. Bedaride}, Regul. Chaotic Dyn. 8, No. 1, 97--104 (2003; Zbl 1023.37024) Full Text: DOI arXiv
Stepin, A. M. On three problems about dynamical systems related to lattices and homogeneous spaces. (English) Zbl 1020.37038 J. Dyn. Control Syst. 9, No. 2, 257-264 (2003). Reviewer: Nikolai Chernov (Birmingham (Alabama)) MSC: 37J35 37-02 37D50 PDFBibTeX XMLCite \textit{A. M. Stepin}, J. Dyn. Control Syst. 9, No. 2, 257--264 (2003; Zbl 1020.37038) Full Text: DOI
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)
Weiss, Barak Dynamics on parameter spaces: submanifold and fractal subset questions. (English) Zbl 1048.37005 Burger, Marc (ed.) et al., Rigidity in dynamics and geometry. Contributions from the programme Ergodic theory, geometric rigidity and number theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, UK, January 5–July 7, 2000. Berlin: Springer (ISBN 3-540-43243-4/hbk). 425-440 (2002). Reviewer: Manuel Sanchis (Castelló) MSC: 37A17 11J83 22F30 37C85 37D40 PDFBibTeX XMLCite \textit{B. Weiss}, in: Rigidity in dynamics and geometry. Contributions from the programme Ergodic theory, geometric rigidity and number theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, UK, January 5--July 7, 2000. Berlin: Springer. 425--440 (2002; Zbl 1048.37005)
Gutkin, Eugene; Judge, Chris Affine mappings of translation surfaces: Geometry and arithmetic. (English) Zbl 0965.30019 Duke Math. J. 103, No. 2, 191-213 (2000). Reviewer: A.P.Stone (Albuquerque) MSC: 30F60 37D50 53D25 30F30 11F72 PDFBibTeX XMLCite \textit{E. Gutkin} and \textit{C. Judge}, Duke Math. J. 103, No. 2, 191--213 (2000; Zbl 0965.30019) Full Text: DOI
Kenyon, Richard; Smillie, John Billiards on rational-angled triangles. (English) Zbl 0967.37019 Comment. Math. Helv. 75, No. 1, 65-108 (2000). Reviewer: Nikolai Chernov (Birmingham (Alabama)) MSC: 37D40 37J35 37D50 PDFBibTeX XMLCite \textit{R. Kenyon} and \textit{J. Smillie}, Comment. Math. Helv. 75, No. 1, 65--108 (2000; Zbl 0967.37019) Full Text: DOI
Grémaud, Benoît; Jain, Sudhir R. Spacing distributions for rhombus billiards. (English) Zbl 0948.37025 J. Phys. A, Math. Gen. 31, No. 37, L637-L643 (1998). MSC: 37D50 37H10 PDFBibTeX XMLCite \textit{B. Grémaud} and \textit{S. R. Jain}, J. Phys. A, Math. Gen. 31, No. 37, L637--L643 (1998; Zbl 0948.37025) Full Text: DOI arXiv
Hiemer, Philipp; Snurnikov, Vadim Polygonal billiards with small obstacles. (English) Zbl 0995.37019 J. Stat. Phys. 90, No. 1-2, 453-466 (1998). Reviewer: Messoud Efendiev (Berlin) MSC: 37D40 PDFBibTeX XMLCite \textit{P. Hiemer} and \textit{V. Snurnikov}, J. Stat. Phys. 90, No. 1--2, 453--466 (1998; Zbl 0995.37019) Full Text: DOI
Eskin, Alex Counting problems and semisimple groups. (English) Zbl 0901.11029 Doc. Math., Extra Vol. ICM Berlin 1998, vol. II, 539-552 (1998). Reviewer: B.Z.Moroz (Bonn) MSC: 11P21 22E40 11J25 11H50 22D40 81Q50 PDFBibTeX XMLCite \textit{A. Eskin}, Doc. Math. Extra Vol., 539--552 (1998; Zbl 0901.11029) Full Text: EuDML EMIS
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
Vorobets, Ya. B. Planar structures and billiards in rational polygons. (English. Russian original) Zbl 0882.58030 Russ. Math. Surv. 51, No. 1, 177-178 (1996); translation from Usp. Mat. Nauk 51, No. 1, 145-146 (1996). Reviewer: W.J.Satzer jun.(St.Paul) MSC: 37A99 PDFBibTeX XMLCite \textit{Ya. B. Vorobets}, Russ. Math. Surv. 51, No. 1, 177--178 (1996; Zbl 0882.58030); translation from Usp. Mat. Nauk 51, No. 1, 145--146 (1996) Full Text: DOI
Masur, Howard Teichmüller space, dynamics, probability. (English) Zbl 0839.32010 Chatterji, S. D. (ed.), Proceedings of the international congress of mathematicians, ICM ’94, August 3-11, 1994, Zürich, Switzerland. Vol. II. Basel: Birkhäuser. 836-849 (1995). MSC: 32G15 37A99 60G50 PDFBibTeX XMLCite \textit{H. Masur}, in: Proceedings of the international congress of mathematicians, ICM '94, August 3-11, 1994, Zürich, Switzerland. Vol. II. Basel: Birkhäuser. 836--849 (1995; Zbl 0839.32010)
Masur, Howard Closed trajectories for quadratic differentials with an application to billiards. (English) Zbl 0616.30044 Duke Math. J. 53, 307-314 (1986). Reviewer: Li Zhong MSC: 30F30 30F99 32G15 PDFBibTeX XMLCite \textit{H. Masur}, Duke Math. J. 53, 307--314 (1986; Zbl 0616.30044) 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