Shortest distance between (random) orbits

Jerome Rousseau (UFBA)

We study the shortest distance between two orbit segments of length n for rapidly mixing dynamical systems. We will show that the asymptotic behavior is given by the correlation dimension of the invariant measure. For the shift map, we will show that this problem corresponds to a well-known sequences matching problem: the longest common substring problem. We will also extend this study to the realm of random dynamical systems and explain the difference between the annealed and quenched version of this problem. This includes some joint works with Vanessa Barros, Adriana Coutinho, Sebastien Gouezel, Rodrigo Lambert, Lingmin Liao and Manuel Stadlbauer.