Targets and Holes

P Giulietti (1) , P Koltai (2) , Sandro Vaienti (3, 4)

1 SNS - Scuola Normale Superiore di Pisa
2 Department of Mathematics and Computer Science
3 CPT - Centre de Physique Théorique - UMR 7332
4 CPT - E7 Systèmes dynamiques : théories et applications

We address the extreme value problem of a one-dimensional dynamical system approaching a fixed target while constrained to avoid a fixed set-which can be thought of as a small hole. The presence of the latter influences the extremal index which will now depend explicitly on the escape rate.

Domaines: Systèmes dynamiques [math.DS]

P Giulietti, P Koltai, Sandro Vaienti. Targets and Holes. Proceedings of the American Mathematical Society, 2021, 149 (8), pp.3293-3306. ⟨10.1090/proc/15384⟩. ⟨hal-02450474⟩