Jérôme ROUSSEAU


Associate Professor

Departamento de Matemática
Universidade Federal da Bahia
Avenida Ademar de Barros s/n
40170-110 Salvador, BA
Brazil
 
E-mail:

Curriculo Lattes
Id orcid.org/0000-0003-3175-1176
Research

My fields of specialization are Ergodic Theory/Dynamical Systems and Probability. My research activity mainly concerns the quantitative study of the long-term behaviour of orbits (for rapidly mixing systems, random dynamical systems and flows) and Sequence Matching Problems, with emphasis in Poincaré recurrence, Hitting/Return times Statistics, Shortest Distance between Orbits, Extreme Value Theory, Dimension Theory and the Longest Common Substring Problem.


Publications/Preprints
  1. Minimal distance between random orbits, Sébastien Gouëzel, J. Rousseau and Manuel Stadlbauer, to appear in Probability Theory and related Fields (pdf)
  2. Orbits closeness for slowly mixing dynamical systems, J. Rousseau and M. Todd, Ergodic Theory & Dynamical Systems, published online (2023) (pdf)
  3. Longest common substring for random subshifts of finite type, J. Rousseau, Ann. Inst. Henri Poincaré Probab. Stat 57 (2021), no. 3, 1768-1785 (pdf)
  4. Rényi entropy and pattern matching for run-length encoded sequences, J. Rousseau, ALEA, Lat. Am. J. Probab. Math. Stat. 18 (2021) 887-905 (pdf)
  5. Shortest distance between multiple orbits and generalized fractal dimensions, V. Barros and J. Rousseau, Ann. Henri Poincaré 22 (2021), no.6, 1853-1885 (pdf)
  6. Exponential Law for Random  Maps  on Compact Manifolds, N. Haydn, J. Rousseau and F. Yang, Nonlinearity 33 (2020), no. 12, 6760-6789 (pdf)
  7. Matching strings in encoded sequences, A. Coutinho, R Lambert and J. Rousseau, Bernoulli 26 (2020), no. 3, 2021-2050. (pdf)
  8. On the shortest distance between orbits and the longest common substring problem, V. Barros, L. Liao and J. Rousseau, Advances in Mathematics 344(2019), 311-339 (pdf)
  9. Large deviation for return times, A. Coutinho, J. Rousseau and B. Saussol, Nonlinearity 31 (2018), no. 11, 5162–5179 (pdf)
  10. Concentration inequalities for sequential dynamical systems of the unit interval, R. Aimino and J. Rousseau, Ergodic Theory & Dynamical Systems 36 (2016), no. 8, 2384-2407 (pdf)
  11. Hitting times and periodicity in random dynamics, J. Rousseau and M. Todd, Journal of Statistical Physics 161 (2015), no. 1, 131-150 (pdf)
  12. Skew products, quantitative recurrence, shrinking targets and decay of correlations, S. Galatolo, J. Rousseau and B. Saussol, Ergodic Theory & Dynamical Systems 35 (2015), no. 6, 1814-1845 (pdf)
  13. Hitting time statistics for observations of dynamical systems, J. Rousseau, Nonlinearity 27 (2014), 2377-2392 (pdf)
  14. Exponential law for random subshifts of finite type, J. Rousseau, B. Saussol and P. Varandas, Stochastic Processes and their Applications 124(2014), no. 10, 3260-3276 (pdf)
  15. Recurrence rates for observations of flows, J. Rousseau,  Ergodic Theory & Dynamical Systems 32 (2012), no. 5, 1727-1751 (pdf)
  16. Entropy formulas for dynamical systems with mistakes, J. Rousseau and P. Varandas and Y. Zhao, Discrete Contin. Dyn. Syst. 32 (2012), no.12, 4391-4407 (pdf)
  17. Recurrence for random dynamical systems, P. Marie and J. Rousseau, Discrete Contin. Dyn. Syst. 30 (2011), no.1, 1-16 (pdf)
  18. Poincaré recurrence for observations, J.Rousseau and B.Saussol, Transactions of the American Mathematical Society 362 (2010), no. 11, 5845-5859 (pdf)



PhD and Habilitation Thesis
-Étude quantitative du comportement à long terme des orbites: récurrence de Poincaré et plus petite distance (pdf)
Habilitation à diriger des recherches, soutenue le 14 avril 2021 à l'Université de Rennes 1

-Récurrence de Poincaré pour les observations (pdf)
Thése de doctorat, soutenue en 2010 sous la direction de Benoit Saussol


Ensino

Listas de exercícios: