Averaged number of visits

Sandro Vaienti (1, 2) , Nicolai Haydn (3) , Enrico Lunedei (4)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332
3 USC - University of Southern California
4 Via G. Milli 2, 47900 Rimini, Italy

We introduce a new indicator for dynamical systems, namely the averaged number of visits, to estimate the frequency of visits in small regions when a map is iterated up to the inverse of the measure of this region. We compute this quantity analytically and numerically for various systems and we show that it depends on the ergodic properties of the systems and on their topological properties, such as the presence of periodic points.

Domaines: Systèmes dynamiques [math.DS]

Sandro Vaienti, Nicolai Haydn, Enrico Lunedei. Averaged number of visits. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2007, 17 (3), pp.033119. ⟨10.1063/1.2771067⟩. ⟨hal-00476241⟩