Serge E. Troubetzkoy
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- Invariant measures for typical continuous maps on manifolds (with E.Catsigeras)
- Pseudo-physical measures for typical continuous maps of the interval (with E.Catsigeras)
List of Publications
- λ-stability of periodic billiard orbits (with J.P. Gaiväo) Nonlinearity (2018)
- Topologically weakly mixing polygonal billiards (with J. Bobok) Proceedings American Mathematical Society (2018)
- On the Hausdorff dimension of minimal interval exchange transformations with flips (with A. Skripchenko) Journal London Mathematical Society (2018)
- Infinite ergodic index of the Ehrenfest wind-tree model (with A. Malaga Sabogal) Communications in Mathematical Physics 358 (2018) 995-1006.
- Weakly mixing polygonal billiards (with A. Malaga Sabogal) Bulletin London Mathematical Society 49 (2017) 141-147.
- Residual generic ergodicity of periodic group extensions over translation surfaces (with D. Ralston) Geometriae Dedicata
187 (2017) 219-239.
- Ergodicity of the Ehrenfest Wind-Tree model (with A. Malaga Sabogal) C. R. Acad. Sci. Paris 354 (2016) 1032-1036.
- Minimality of the Ehrenfest Wind-Tree model (with A. Malaga Sabogal) Journal Modern Dynamics 10 (2016) 209-228.
- Multiple mixing from weak hyperbolicity by the Hopf argument
(with Y. Coudčne and B. Hasselblatt)
Stochastics and Dynamics 16 (2016) 15pp
- Entropy and complexity of polygonal billiards with spy mirrors (with A. Skripchenko) Nonlinearity 28 (2015) 3443-3456.
- Polygonal billiards with one sided scattering (with A. Skripchenko) Annales de l'Insitut Fourier 65 (2015) 1881-1896.
- Homotopical rigidity of polygonal billiards (with J. Bobok) Toplogy and its Applications 173 (2014) 308-324.
- Dynamical diophantine approximation (with A.-H. Fan and J. Schmeling) Proceedings of the London Mathematical Society 107 (2013) 1173-1219.
- Orbit structure of interval exchange transformations with flips (with A. Nogueira and B. Pires) Nonlinearity 26 (2013) 525-537.
- Ergodicity of certain cocyles over certain interval exchanges (with D. Ralston) Discrete and Continuous Dynamical Systems 33 (2013) 2523-2529.
- Ergodic infinite group extensions of geodesic flows on translation surfaces (with D. Ralston) Journal of Modern Dynamics 6 (2012) 477-497.
- Recurrence in generic staircases Discrete and Continuous Dynamical Systems 32 (2012) 1047-1053.
- Code & Order in polygonal billiards (with J. Bobok) Topology and its Applications 159 (2012) 236-247.
- Infinite - horizon Lorentz tubes and gases: recurrence and ergodic properties (with M. Lenci) Physica D 240 (2011) 1510-1515.
- Coding Discretizations of Continuous Functions (with C. Rojas)
Discrete Mathematics 31 (2011) 620-627.
- Does a billiard orbit determine its (polygonal) table? (with J. Bobok) Fundamenta Mathematicae 212 (2011) 129-144.
- Topological and symbolic dynamics for hyperbolic systems with holes (with S. Bundfuss and T. Krueger) Ergodic Theory and Dynamical Systems 31 (2011) 1305-1323.
- 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.
- 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.
- 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 (with P. Balint) Nonlinearity 17 (2004) 2069-2090. PS PDF
- 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)