Serge E. Troubetzkoy

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Telephone: 04.91.26.96.66

Fax: 04.91.26.95.04

Preprints

  1. Complexity for billiards in regular N-gons (with J. Athreya, and P. Hubert) PDF
  2. The generic continuous Lebesgue measure preserving interval map is nowhere monotone but invertible a.e. (with J. Bobok, J. Činč, and P. Oprocha) PDF
  3. On the complexity of polygonal billiards) (with A. Noguiera and T. Krueger) PDF
  4. Interval maps with dense periodicity (with J. Bobok, J. Činč, and P. Oprocha) PDF

List of Publications

  1. Unique ergodicity for infinite area Translation Surfaces (with A. Malaga Sabogal) Nonlinearity (2025+) PDF
  2. Ergodic measure with infinite entropy (with E. Catsigeras) Fund. Math. 266 (2024), no. 2, 121–166. PDF
  3. Are generic dynamical properties stable under composition with rotations? (with J. Bobok, J. Činč, and P. Oprocha) Proc. AMS 152 (2024), 3011–3026. PDF
  4. Continuous Lebesgue measure-preserving maps on one-dimensional manifolds: a survey (with J. Bobok, J. Činč, and P. Oprocha) to appear in Topology and its Applications PDF
  5. The Horizontal Chord Set (with D. Davis) American Math. Monthly. 131 (2024), 519–525. PDF
  6. An upper bound on topological entropy of the Bunimovich stadium billiard map (with J. Činč) Journal of Statistical Physics J. Stat. Phys. 190 (2023) PDF
  7. Vertex to vertes geodesics on platonic solids American Math. Monthly 130 (2023) 379-382 PDF
  8. Topologically weakly mixing polygonal billiards (with J. Bobok) Proceedings American Mathematical Society 151 (2023) 3391-3400 PDF
  9. Periodic points and shadowing property for generic Lebesgue measure prserving interval maps (with J. Bobok, J. Činč, and P. Oprocha) Nonlinearity 35 (2022) 2535-2558 PDF
  10. Chess billiards (with A. Nogueira) Mathematical Intelligencer 44 (2022) 331-338 PDF
  11. S-limit shadowing is generic for continuous Lebesgue measure prserving circle maps (with J. Bobok, J. Činč, and P. Oprocha) Ergodic Theory and Dynamical Systems 43(2022) 78-98 Open access
  12. The role of continuity and expansiveness on leo and periodic specification properties (with P. Varandas) Proceedings Chair Morlet 2019 CIRM, Lecture Notes in Mathematics 2290, Springer Verlag (2021) PDF
  13. Probabilistic aspects of dynamical systems (with W. Bahsoun, S. Galatolo, Vaienti) Nonlinearity 36 (2020) 6461-6479 PDF
  14. Typical properties of interval maps preserving the Lebesgue measure (with J. Bobok) Nonlinearity 36 (2020) 6461-6479 PDF
  15. Invariant measures for typical continuous maps on manifolds (with E. Catsigeras) Nonlinearity 32 (2019) 3981-4001 PDF
  16. λ-stability of periodic billiard orbits (with J.P. Gaiväo) Nonlinearity 31 (2018) 4326-4353 PDF
  17. On the Hausdorff dimension of minimal interval exchange transformations with flips (with A. Skripchenko) Journal London Mathematical Society 97 (2018) 149-169 PDF
  18. Infinite ergodic index of the Ehrenfest wind-tree model (with A. Malaga Sabogal) Communications in Mathematical Physics 358 (2018) 995-1006 PDF
  19. Weakly mixing polygonal billiards (with A. Malaga Sabogal) Bulletin London Mathematical Society 49 (2017) 141-147 PDF
  20. Residual generic ergodicity of periodic group extensions over translation surfaces (with D. Ralston) Geometriae Dedicata 187 (2017) 219-239 PDF
  21. Ergodicity of the Ehrenfest Wind-Tree model (with A. Malaga Sabogal) C. R. Acad. Sci. Paris 354 (2016) 1032-1036 PDF
  22. Minimality of the Ehrenfest Wind-Tree model (with A. Malaga Sabogal) Journal Modern Dynamics 10 (2016) 209-228 PDF
  23. Multiple mixing from weak hyperbolicity by the Hopf argument (with Y. Coudène and B. Hasselblatt) Stochastics and Dynamics 16 (2016) 15pp PDF
  24. Entropy and complexity of polygonal billiards with spy mirrors (with A. Skripchenko) Nonlinearity 28 (2015) 3443-3456. PDF
  25. Polygonal billiards with one sided scattering (with A. Skripchenko) Annales de l'Insitut Fourier 65 (2015) 1881-1896 PDF
  26. Homotopical rigidity of polygonal billiards (with J. Bobok) Toplogy and its Applications 173 (2014) 308-324 PDF
  27. Dynamical diophantine approximation (with A.-H. Fan and J. Schmeling) Proceedings of the London Mathematical Society 107 (2013) 1173-1219 PDF
  28. Orbit structure of interval exchange transformations with flips (with A. Nogueira and B. Pires) Nonlinearity 26 (2013) 525-537. PDF
  29. Ergodicity of certain cocyles over certain interval exchanges (with D. Ralston) Discrete and Continuous Dynamical Systems 33 (2013) 2523-2529. PDF
  30. Ergodic infinite group extensions of geodesic flows on translation surfaces (with D. Ralston) Journal of Modern Dynamics 6 (2012) 477-497. PDF
  31. Recurrence in generic staircases Discrete and Continuous Dynamical Systems 32 (2012) 1047-1053. PDF
  32. Code & Order in polygonal billiards (with J. Bobok) Topology and its Applications 159 (2012) 236-247. PDF
  33. Infinite - horizon Lorentz tubes and gases: recurrence and ergodic properties (with M. Lenci) Physica D 240 (2011) 1510-1515. PDF
  34. Coding Discretizations of Continuous Functions (with C. Rojas) Discrete Mathematics 31 (2011) 620-627. PDF
  35. Does a billiard orbit determine its (polygonal) table? (with J. Bobok) Fundamenta Mathematicae 212 (2011) 129-144. PDF
  36. Topological and symbolic dynamics for hyperbolic systems with holes (with S. Bundfuss and T. Krüger) Ergodic Theory and Dynamical Systems 31 (2011) 1305-1323. PDF
  37. The Ehrenfest wind-tree model: periodic directions, recurrence, diffusion (with P. Hubert and S. Lelievre) Journal fuer die reine und angewandte Mathematik (Crelle's Journal) 656 (2011) 223-244. PDF
  38. Arbeitsgemeinschaft: Mathematical billiards (with S. Tabachnikov) Oberwolfach Reports 7 (2010) 955-957.
  39. Typical recurrence for the Ehrenfest wind-tree model Journal of Statistical Physics 141 (2010) 60-67. PDF
  40. Approximation and billiards Systèmes dynamiques et approximations diophantiennes, Séminaires et congrès, Société Mathématique de France 20 (2009) 175-187. PS PDF
  41. Dual billiards, Fagnano orbits and regular polygons American Mathematical Monthly 116:3 (2009) 251-260. PS PDF
  42. Modular fibers and illumination problems (with P. Hubert, and M. Schmoll) International Mathematics Research Notices (2008) no. 8 Art. ID rnn011, 42pp.PDF
  43. Quantisations of piecewise affine maps on the torus and their quantum limits (with C.-H. Chang, T. Krüger and R. Schubert) Communications in Mathematical Physics 282 (2008) 395-418. PS PDF
  44. Periodic billiard orbits in right triangles Annales de l'Institut Fourier 55 (2005) 29-46. PS PDF
  45. Rotor interaction in the annulus billiard (2004) (with P. Balint) Journal Statistical Physics 117 (2004) 681--702. PS PDF
  46. Ergodicity of Two Hard Balls in Integrable Polygons (with P. Balint) Nonlinearity 17 (2004) 2069-2090. PS PDF
  47. Recurrence and periodic billiard orbits in polygons, Regular and Chaotic Dynamics 9 (2004) 1-12. PDF PS
  48. The Gauss map on a class of interval translation mappings (with H. Bruin) Israel Journal of Mathematics 137 (2003) 125-148. PS
  49. Recurrence and Lyapunov Exponents (with B. Saussol and S. Vaienti) Moscow Mathematical Journal 3(1) (2003) 189-203. DVI PS
  50. Inhomogeneous Diophantine Approximation and Angular Recurrence for Polygonal Billiards (with J. Schmeling) Mat. Sbornik 194 (2003) 295-309. DVI PS
  51. Return Time Statistics via Inducing (with H. Bruin, B. Saussol and S. Vaienti) Ergodic Theory Dynamical Systems 23 (2003) 991-1013. DVI PS
  52. Billards Polygonaux (with P. Hubert) Le bulletin de la FRUMAM 5 (2003) 7-11.
  53. Absolute quantification of specific nucleic acids by (RT)-PCR using a nonlinear mathematical model for data analysis (with H.L. Vu, H.H. Nguyen, V.Q. Nguyen, M. Russell and J. Mestecky) in PCR Technology: Current Innovations, Second Edition; Thomas Weissensteiner, Annette M. Griffin and Hugh G. Griffin (Editors) CRC Press, 2003.
  54. Complexity and growth for polygonal billiards (with J. Cassaigne and P. Hubert) Annales de l'Institut Fourier 52 (2002) 1001-1013. DVI PS
  55. Recurrence, Dimensions and Lyapunov Exponents (with B. Saussol and S. Vaienti) Journal of Statistical Physics 106 (2002) 623-634. DVI PS
  56. Circles and polygons Geom. Dedic. 80 (2000) 289-295.
  57. Invariant measures for Anosov maps with small holes (with N. Chernov and R. Markarian) Ergodic Theory Dynamical Systems 20 (2000) 1007-1044.
  58. A method for quantification of absolute amounts of nucleic acids by competitive (RT)-PCR and a new mathematical model for data analysis (with H.L. Vu, H.H. Nguyen, M. Russel and J. Mestecky) Nucleic Acids Research Methods 18-7 (2000)
  59. Interval translation maps (with J. Schmeling) in Dynamical Systems From Crystals to Chaos, World Scientific J.M. Gambaudo et.al eds. (2000) 291-302.
  60. Billiards in infinite polygons Nonlinearity 12 (1999) 513-524.
  61. The center problem for nonautonomous dynamical systems, (with T. Krüger and L. Pustilnikov) Bulletin Brazilian Math. Soc. 30 (1999) 1-30.
  62. Ergodicity of billiards in polygons with pockets (with N. Chernov) Nonlinearity 11 (1998) 1095-1102.
  63. Conditionally invariant measures for Anosov maps with small holes, (with N. Chernov and R. Makarian) Ergodic Theory Dynamical Systems 18 (1998) 1049-1073.
  64. Complexity lower bounds for polygonal billiards Chaos 8 (1998) 242-244.
  65. Dimension and invertiblity of hyperbolic endomorphisms with singularities, (with J. Schmeling) Ergodic Theory Dynamical Systems 18 (1998) 1257-1282.
  66. Further travels with my ant (with D. Gale, J. Propp and S. Sutherland) Mathematical Intelligencer as a Mathematical Entertainments Column, 17 (1995). Reprinted in: Tracking the automatic ant and other mathematical explorations by D. Gale, Springer Verlag (1998) NY.
  67. Periodic billiard orbits are dense in rational polygons (with M. Boshernitzan, G. Galperin and T. Krüger) Transactions AMS 350 (1998) 3523-3535.
  68. The Lewis-Parker lecture: The ant, Alabama J. Math. 21 (1997) 3-15.
  69. Complexity, randomness, discretizations and quantum chaos: some remarks on a program of J. Ford, (with T. Krüger) Physica D 105 (1997) 97-104.
  70. Points with infinite Lyapunov exponents and measures of maximal entropy for the Lorentz gas (with N. Chernov) Journal Statistical Physics 83 (1996) 193--202.
  71. Directional flows for polygonal billiards (with E. Gutkin) International Congress of Dynamical Systems, Montevideo (1995) F. Ledrappier, et. al. eds., Longman
  72. Acceleration of bouncing balls in external fields (with T. Krüger and L. Pustilnikov) Nonlinearity 8 (1995) 397--410.
  73. Local instability of orbits in polygonal and polyhedral billiards, (with G. Galperin and T. Krüger) Communications Mathematical Physics 169 (1995) 463--473.
  74. Rotators and periodicity in cyclic cellular automata, (with L.A. Bunimovich) Journal Statistical Physics 74 (1994) 1--14.
  75. Complexity and randomness of recursive discretizations of dynamical systems, (with T. Krüger and P. Seibt) Random and Computational Dynamics 2 (1994) 1--21. PDF
  76. Topological dynamics of flipping Lorentz lattice gas models, (with L.A. Bunimovich) Journal Statistical Physics 72 (1993) 297--308.
  77. Non Gaussian behavior in Lorentz lattice gas cellular automata, (with L.A. Bunimovich) Proceedings: Dynamics of Complex and Irregular Systems, World Scientific, Ph. Blanchard ed. (1993).
  78. Ergodic theory on recursive lattices, a theoretical approach to computer simulations of chaotic systems (with T. Krüger) Proceedings: Dynamics of Complex and Irregular Systems, World Scientific, Ph. Blanchard ed. (1993).
  79. Recurrence properties of Lorentz lattice gas cellular automata, (with L.A. Bunimovich) Journal Statistical Physics 67 (1992) 289--302.
  80. Markov partitions and shadowing for nonuniformly hyperbolic systems with singularities, (with T. Krüger) Ergodic Theory Dynamical Systems 12 (1992) 487--508.
  81. Extreme instability of the horocycle flow, Journal d'Analyse Mathematique 57 (1991) 37--63.
  82. Stochastic stability of scattering billiards, Theoretical and Mathematical Physics 86 (1991) 221--230.
  83. A comparison of elastic and inelastic billiards, Nonlinearity 3 (1990) 947--960
  84. Extreme instability of the horocycle flow, Stanford University PhD thesis (1987).
  85. An efficient implementation of a context dependent lossless speech compression scheme, (with G. Langdon) IBM Technical Disclosure Bulletin SA8-85-0284 (1985)

Unpublished Articles

  1. Pseudo-physical measures for typical continuous maps of the interval (with E. Catsigeras) PDF