A notion of Denjoy sub-system

Marie-Claude Arnaud (1) , Patrice Le Calvez (2)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 UPMC - Université Pierre et Marie Curie - Paris 6

We introduce a notion of Denjoy sub-system that generalizes the one of Aubry-Mather set. For such systems, we prove a result similar to Denjoy theorem (non-existence of C2 Denjoy sub-systems), and study their Lyapunov exponents.

Keywords: Denjoy theorem; Cantor sets; Lyapunov exponents; Aubry-Mather sets

Domains: Mathematics [math]; Dynamical Systems [math.DS]

Marie-Claude Arnaud, Patrice Le Calvez. A notion of Denjoy sub-system. 2017. ⟨hal-01567649⟩