Asymptotically periodic piecewise contractions of the interval

Arnaldo Nogueira (1) , Benito Pires (2) , Rafael A. Rosales (2)

1 I2M - Institut de Mathématiques de Marseille
2 USP - Universidade de São Paulo = University of São Paulo

We consider the iterates of a generic injective piecewise contraction of the interval defined by a finite family of contractions. Let $\phi_i:[0,1]\to (0,1)$, $1\le i\le n$, be $C^2$-diffeomorphisms with $\sup_{x\in (0,1)} \vert D\phi_i(x)\vert<1$ whose images $\phi_1([0,1]), \ldots, \phi_n([0,1])$ are pairwise disjoint. Let $0

Mots clés: piecewise contraction of the interval; topological dynamics; periodic orbit; ergodic theory

Domaines: Systèmes dynamiques [math.DS]

Arnaldo Nogueira, Benito Pires, Rafael A. Rosales. Asymptotically periodic piecewise contractions of the interval. Nonlinearity, 2014, 27 (7), pp.1603--1610. ⟨10.1088/0951-7715/27/7/1603⟩. ⟨hal-01341987⟩