Serge E. Troubetzkoy

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

List of Publications

  1. λ-stability of periodic billiard orbits (with J.P. Gaiväo) Nonlinearity (2018) PDF
  2. Topologically weakly mixing polygonal billiards (with J. Bobok) Proceedings American Mathematical Society (2018) PDF
  3. On the Hausdorff dimension of minimal interval exchange transformations with flips (with A. Skripchenko) Journal London Mathematical Society (2018) PDF
  4. Infinite ergodic index of the Ehrenfest wind-tree model (with A. Malaga Sabogal) Communications in Mathematical Physics 358 (2018) 995-1006. PDF
  5. Weakly mixing polygonal billiards (with A. Malaga Sabogal) Bulletin London Mathematical Society 49 (2017) 141-147. PDF
  6. Residual generic ergodicity of periodic group extensions over translation surfaces (with D. Ralston) Geometriae Dedicata 187 (2017) 219-239. PDF
  7. Ergodicity of the Ehrenfest Wind-Tree model (with A. Malaga Sabogal) C. R. Acad. Sci. Paris 354 (2016) 1032-1036. PDF
  8. Minimality of the Ehrenfest Wind-Tree model (with A. Malaga Sabogal) Journal Modern Dynamics 10 (2016) 209-228. PDF
  9. Multiple mixing from weak hyperbolicity by the Hopf argument (with Y. Coudčne and B. Hasselblatt) Stochastics and Dynamics 16 (2016) 15pp PDF
  10. Entropy and complexity of polygonal billiards with spy mirrors (with A. Skripchenko) Nonlinearity 28 (2015) 3443-3456. PDF
  11. Polygonal billiards with one sided scattering (with A. Skripchenko) Annales de l'Insitut Fourier 65 (2015) 1881-1896. PDF
  12. Homotopical rigidity of polygonal billiards (with J. Bobok) Toplogy and its Applications 173 (2014) 308-324. PDF
  13. Dynamical diophantine approximation (with A.-H. Fan and J. Schmeling) Proceedings of the London Mathematical Society 107 (2013) 1173-1219. PDF
  14. Orbit structure of interval exchange transformations with flips (with A. Nogueira and B. Pires) Nonlinearity 26 (2013) 525-537. PDF
  15. Ergodicity of certain cocyles over certain interval exchanges (with D. Ralston) Discrete and Continuous Dynamical Systems 33 (2013) 2523-2529. PDF
  16. Ergodic infinite group extensions of geodesic flows on translation surfaces (with D. Ralston) Journal of Modern Dynamics 6 (2012) 477-497. PDF
  17. Recurrence in generic staircases Discrete and Continuous Dynamical Systems 32 (2012) 1047-1053. PDF
  18. Code & Order in polygonal billiards (with J. Bobok) Topology and its Applications 159 (2012) 236-247. PDF
  19. Infinite - horizon Lorentz tubes and gases: recurrence and ergodic properties (with M. Lenci) Physica D 240 (2011) 1510-1515. PDF
  20. Coding Discretizations of Continuous Functions (with C. Rojas) Discrete Mathematics 31 (2011) 620-627. PDF
  21. Does a billiard orbit determine its (polygonal) table? (with J. Bobok) Fundamenta Mathematicae 212 (2011) 129-144. PDF
  22. 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
  23. 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
  24. Arbeitsgemeinschaft: Mathematical billiards (with S. Tabachnikov) Oberwolfach Reports 7 (2010) 955-957.
  25. Typical recurrence for the Ehrenfest wind-tree model Journal of Statistical Physics 141 (2010) 60-67. PDF
  26. Approximation and billiards Systčmes dynamiques et approximations diophantiennes, Séminaires et congrčs, Société Mathématique de France 20 (2009) 175-187. PS PDF
  27. Dual billiards, Fagnano orbits and regular polygons American Mathematical Monthly 116:3 (2009) 251-260. PS PDF
  28. Modular fibers and illumination problems (with P. Hubert, and M. Schmoll) International Mathematics Research Notices (2008) no. 8 Art. ID rnn011, 42pp.PDF
  29. 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
  30. Periodic billiard orbits in right triangles Annales de l'Institut Fourier 55 (2005) 29-46. PS PDF
  31. Rotor interaction in the annulus billiard (2004) (with P. Balint) Journal Statistical Physics 117 (2004) 681--702. PS PDF
  32. Ergodicity of Two Hard Balls in Integrable Polygons (with P. Balint) Nonlinearity 17 (2004) 2069-2090. PS PDF
  33. Recurrence and periodic billiard orbits in polygons, Regular and Chaotic Dynamics 9 (2004) 1-12. PDF PS
  34. The Gauss map on a class of interval translation mappings (with H. Bruin) Israel Journal of Mathematics 137 (2003) 125-148. PS
  35. Recurrence and Lyapunov Exponents (with B. Saussol and S. Vaienti) Moscow Mathematical Journal 3(1) (2003) 189-203. DVI PS
  36. Inhomogeneous Diophantine Approximation and Angular Recurrence for Polygonal Billiards (with J. Schmeling) Mat. Sbornik 194 (2003) 295-309. DVI PS
  37. Return Time Statistics via Inducing (with H. Bruin, B. Saussol and S. Vaienti) Ergodic Theory Dynamical Systems 23 (2003) 991-1013. DVI PS
  38. Billards Polygonaux (with P. Hubert) Le bulletin de la FRUMAM 5 (2003) 7-11.
  39. 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.
  40. Complexity and growth for polygonal billiards (with J. Cassaigne and P. Hubert) Annales de l'Institut Fourier 52 (2002) 1001-1013. DVI PS
  41. Recurrence, Dimensions and Lyapunov Exponents (with B. Saussol and S. Vaienti) Journal of Statistical Physics 106 (2002) 623-634. DVI PS
  42. Circles and polygons Geom. Dedic. 80 (2000) 289-295.
  43. Invariant measures for Anosov maps with small holes (with N. Chernov and R. Markarian) Ergodic Theory Dynamical Systems 20 (2000) 1007-1044.
  44. 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)
  45. Interval translation maps (with J. Schmeling) in Dynamical Systems From Crystals to Chaos, World Scientific J.M. Gambaudo eds. (2000) 291-302.
  46. Billiards in infinite polygons Nonlinearity 12 (1999) 513-524.
  47. The center problem for nonautonomous dynamical systems, (with T. Krüger and L. Pustilnikov) Bulletin Brazilian Math. Soc. 30 (1999) 1-30.
  48. Ergodicity of billiards in polygons with pockets (with N. Chernov) Nonlinearity 11 (1998) 1095-1102.
  49. Conditionally invariant measures for Anosov maps with small holes, (with N. Chernov and R. Makarian) Ergodic Theory Dynamical Systems 18 (1998) 1049-1073.
  50. Complexity lower bounds for polygonal billiards Chaos 8 (1998) 242-244.
  51. Dimension and invertiblity of hyperbolic endomorphisms with singularities, (with J. Schmeling) Ergodic Theory Dynamical Systems 18 (1998) 1257-1282.
  52. 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.
  53. Periodic billiard orbits are dense in rational polygons (with M. Boshernitzan, G. Galperin and T. Krüger) Transactions AMS 350 (1998) 3523-3535.
  54. The Lewis-Parker lecture: The ant, Alabama J. Math. 21 (1997) 3-15.
  55. Complexity, randomness, discretizations and quantum chaos: some remarks on a program of J. Ford, (with T. Krüger) Physica D 105 (1997) 97-104.
  56. Points with infinite Lyapunov exponents and measures of maximal entropy for the Lorentz gas (with N. Chernov) Journal Statistical Physics 83 (1996) 193--202.
  57. Directional flows for polygonal billiards (with E. Gutkin) International Congress of Dynamical Systems, Montevideo (1995) F. Ledrappier, et. al. eds., Longman
  58. Acceleration of bouncing balls in external fields (with T. Krüger and L. Pustilnikov) Nonlinearity 8 (1995) 397--410.
  59. Local instability of orbits in polygonal and polyhedral billiards, (with G. Galperin and T. Krüger) Communications Mathematical Physics 169 (1995) 463--473.
  60. Rotators and periodicity in cyclic cellular automata, (with L.A. Bunimovich) Journal Statistical Physics 74 (1994) 1--14.
  61. Complexity and randomness of recursive discretizations of dynamical systems, (with T. Krüger and P. Seibt) Random and Computational Dynamics 2 (1994) 1--21. PDF
  62. Topological dynamics of flipping Lorentz lattice gas models, (with L.A. Bunimovich) Journal Statistical Physics 72 (1993) 297--308.
  63. 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).
  64. 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).
  65. Recurrence properties of Lorentz lattice gas cellular automata, (with L.A. Bunimovich) Journal Statistical Physics 67 (1992) 289--302.
  66. Markov partitions and shadowing for nonuniformly hyperbolic systems with singularities, (with T. Krüger) Ergodic Theory Dynamical Systems 12 (1992) 487--508.
  67. Extreme instability of the horocycle flow, Journal d'Analyse Mathematique 57 (1991) 37--63.
  68. Stochastic stability of scattering billiards, Theoretical and Mathematical Physics 86 (1991) 221--230.
  69. A comparison of elastic and inelastic billiards, Nonlinearity 3 (1990) 947--960
  70. Extreme instability of the horocycle flow, Stanford University PhD thesis (1987).
  71. An efficient implementation of a context dependent lossless speech compression scheme, (with G. Langdon) IBM Technical Disclosure Bulletin SA8-85-0284 (1985)