**Serge E. Troubetzkoy**

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Telephone: 04.91.26.96.66

Fax: 04.91.26.95.04

**Preprints**

**Invariant measures for typical continuous maps on manifolds**(with E.Catsigeras) PDF**Pseudo-physical measures for typical continuous maps of the interval**(with E.Catsigeras) PDF

**List of Publications**

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