Serge E. Troubetzkoy

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Telephone: 04.91.26.96.66

Fax: 04.91.26.95.04

Preprints

  1. Pseudo-physical measures for typical continuous maps of the interval (with E.Catsigeras) PDF
  2. Topologically weakly mixing polygonal billiards (with J. Bobok) PDF
  3. Infinite ergodic index of the Ehrenfest wind-tree model (with A. Malaga Sabogal) PDF
  4. λ-stability of periodic billiard orbits (with J.P. Gaiväo) PDF
  5. On the Hausdorff dimension of minimal interval exchange transformations with flips (with A. Skripchenko) PDF

List of Publications


  1. Weakly mixing polygonal billiards (with A. Malaga Sabogal) Bulletin London Mathematical Society 49 (2017) 141-147. PDF
  2. Residual generic ergodicity of periodic group extensions over translation surfaces (with D. Ralston) Geometriae Dedicata 187 (2017) 219-239. PDF
  3. Ergodicity of the Ehrenfest Wind-Tree model (with A. Malaga Sabogal) C. R. Acad. Sci. Paris 354 (2016) 1032-1036. PDF
  4. Minimality of the Ehrenfest Wind-Tree model (with A. Malaga Sabogal) Journal Modern Dynamics 10 (2016) 209-228. PDF
  5. Multiple mixing from weak hyperbolicity by the Hopf argument Stochastics and Dynamics 16 (2016) 15pp (with Y. Coudčne and B. Hasselblatt) PDF
  6. Entropy and complexity of polygonal billiards with spy mirrors (with A. Skripchenko) Nonlinearity 28 (2015) 3443-3456. PDF
  7. Polygonal billiards with one sided scattering (with A. Skripchenko) Annales de l'Insitut Fourier 65 (2015) 1881-1896. PDF
  8. Homotopical rigidity of polygonal billiards (with J. Bobok) Toplogy and its Applications 173 (2014) 308-324. PDF
  9. Dynamical diophantine approximation (with A.-H. Fan and J. Schmeling) Proceedings of the London Mathematical Society 107 (2013) 1173-1219. PDF
  10. Orbit structure of interval exchange transformations with flips (with A. Nogueira and B. Pires) Nonlinearity 26 (2013) 525-537. PDF
  11. Ergodicity of certain cocyles over certain interval exchanges (with D. Ralston) Discrete and Continuous Dynamical Systems 33 (2013) 2523-2529. PDF
  12. Ergodic infinite group extensions of geodesic flows on translation surfaces (with D. Ralston) Journal of Modern Dynamics 6 (2012) 477-497. PDF
  13. Recurrence in generic staircases Discrete and Continuous Dynamical Systems 32 (2012) 1047-1053. PDF
  14. Code & Order in polygonal billiards (with J. Bobok) Topology and its Applications 159 (2012) 236-247. PDF
  15. Infinite - horizon Lorentz tubes and gases: recurrence and ergodic properties (with M. Lenci) Physica D 240 (2011) 1510-1515. PDF
  16. Coding Discretizations of Continuous Functions (with C. Rojas) Discrete Mathematics 31 (2011) 620-627. PDF
  17. Does a billiard orbit determine its (polygonal) table? (with J. Bobok) Fundamenta Mathematicae 212 (2011) 129-144. PDF
  18. Topological and symbolic dynamics for hyperbolic systems with holes (with S. Bundfuss and T. Krueger) Ergodic Theory and Dynamical Systems 31 (2011) 1305-1323. PDF
  19. 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
  20. Arbeitsgemeinschaft: Mathematical billiards (with S. Tabachnikov) Oberwolfach Reports 7 (2010) 955-957.
  21. Typical recurrence for the Ehrenfest wind-tree model Journal of Statistical Physics 141 (2010) 60-67. PDF
  22. Approximation and billiards Systčmes dynamiques et approximations diophantiennes, Séminaires et congrčs, Société Mathématique de France 20 (2009) 175-187. PS PDF
  23. Dual billiards, Fagnano orbits and regular polygons American Mathematical Monthly 116:3 (2009) 251-260. PS PDF
  24. Modular fibers and illumination problems (with P. Hubert, and M. Schmoll) International Mathematics Research Notices (2008) no. 8 Art. ID rnn011, 42pp.PDF
  25. Quantisations of piecewise affine maps on the torus and their quantum limits (with C.-H. Chang, T. Krueger and R. Schubert) Communications in Mathematical Physics 282 (2008) 395-418. PS PDF
  26. Periodic billiard orbits in right triangles Annales de l'Institut Fourier 55 (2005) 29-46. PS PDF
  27. Rotor interaction in the annulus billiard (2004) (with P. Balint) Journal Statistical Physics 117 (2004) 681--702. PS PDF
  28. Ergodicity of Two Hard Balls in Integrable Polygons (with P. Balint) Nonlinearity 17 (2004) 2069-2090. PS PDF
  29. Recurrence and periodic billiard orbits in polygons, Regular and Chaotic Dynamics 9 (2004) 1-12. PDF PS
  30. The Gauss map on a class of interval translation mappings (with H. Bruin) Israel Journal of Mathematics 137 (2003) 125-148. PS
  31. Recurrence and Lyapunov Exponents (with B. Saussol and S. Vaienti) Moscow Mathematical Journal 3(1) (2003) 189-203. DVI PS
  32. Inhomogeneous Diophantine Approximation and Angular Recurrence for Polygonal Billiards (with J. Schmeling) Mat. Sbornik 194 (2003) 295-309. DVI PS
  33. Return Time Statistics via Inducing (with H. Bruin, B. Saussol and S. Vaienti) Ergodic Theory Dynamical Systems 23 (2003) 991-1013. DVI PS
  34. Billards Polygonaux (with P. Hubert) Le bulletin de la FRUMAM 5 (2003) 7-11.
  35. 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.
  36. Complexity and growth for polygonal billiards (with J. Cassaigne and P. Hubert) Annales de l'Institut Fourier 52 (2002) 1001-1013. DVI PS
  37. Recurrence, Dimensions and Lyapunov Exponents (with B. Saussol and S. Vaienti) Journal of Statistical Physics 106 (2002) 623-634. DVI PS
  38. Circles and polygons Geom. Dedic. 80 (2000) 289-295.
  39. Invariant measures for Anosov maps with small holes (with N. Chernov and R. Markarian) Ergodic Theory Dynamical Systems 20 (2000) 1007-1044.
  40. 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)
  41. Interval translation maps (with J. Schmeling) in Dynamical Systems From Crystals to Chaos, World Scientific J.M. Gambaudo et.al eds. (2000) 291-302.
  42. Billiards in infinite polygons Nonlinearity 12 (1999) 513-524.
  43. The center problem for nonautonomous dynamical systems, (with T. Krüger and L. Pustilnikov) Bulletin Brazilian Math. Soc. 30 (1999) 1-30.
  44. Ergodicity of billiards in polygons with pockets (with N. Chernov) Nonlinearity 11 (1998) 1095-1102.
  45. Conditionally invariant measures for Anosov maps with small holes, (with N. Chernov and R. Makarian) Ergodic Theory Dynamical Systems 18 (1998) 1049-1073.
  46. Complexity lower bounds for polygonal billiards Chaos 8 (1998) 242-244.
  47. Dimension and invertiblity of hyperbolic endomorphisms with singularities, (with J. Schmeling) Ergodic Theory Dynamical Systems 18 (1998) 1257-1282.
  48. 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.
  49. Periodic billiard orbits are dense in rational polygons (with M. Boshernitzan, G. Galperin and T. Krüger) Transactions AMS 350 (1998) 3523-3535.
  50. The Lewis-Parker lecture: The ant, Alabama J. Math. 21 (1997) 3-15.
  51. Complexity, randomness, discretizations and quantum chaos: some remarks on a program of J. Ford, (with T. Krüger) Physica D 105 (1997) 97-104.
  52. Points with infinite Lyapunov exponents and measures of maximal entropy for the Lorentz gas (with N. Chernov) Journal Statistical Physics 83 (1996) 193--202.
  53. Directional flows for polygonal billiards (with E. Gutkin) International Congress of Dynamical Systems, Montevideo (1995) F. Ledrappier, et. al. eds., Longman
  54. Acceleration of bouncing balls in external fields (with T. Krüger and L. Pustilnikov) Nonlinearity 8 (1995) 397--410.
  55. Local instability of orbits in polygonal and polyhedral billiards, (with G. Galperin and T. Krüger) Communications Mathematical Physics 169 (1995) 463--473.
  56. Rotators and periodicity in cyclic cellular automata, (with L.A. Bunimovich) Journal Statistical Physics 74 (1994) 1--14.
  57. Complexity and randomness of recursive discretizations of dynamical systems, (with T. Krüger and P. Seibt) Random and Computational Dynamics 2 (1994) 1--21. PDF
  58. Topological dynamics of flipping Lorentz lattice gas models, (with L.A. Bunimovich) Journal Statistical Physics 72 (1993) 297--308.
  59. 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).
  60. 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).
  61. Recurrence properties of Lorentz lattice gas cellular automata, (with L.A. Bunimovich) Journal Statistical Physics 67 (1992) 289--302.
  62. Markov partitions and shadowing for nonuniformly hyperbolic systems with singularities, (with T. Krüger) Ergodic Theory Dynamical Systems 12 (1992) 487--508.
  63. Extreme instability of the horocycle flow, Journal d'Analyse Mathematique 57 (1991) 37--63.
  64. Stochastic stability of scattering billiards, Theoretical and Mathematical Physics 86 (1991) 221--230.
  65. A comparison of elastic and inelastic billiards, Nonlinearity 3 (1990) 947--960
  66. Extreme instability of the horocycle flow, Stanford University PhD thesis (1987).
  67. An efficient implementation of a context dependent lossless speech compression scheme, (with G. Langdon) IBM Technical Disclosure Bulletin SA8-85-0284 (1985)