Dynamics of piecewise contractions of the interval

Arnaldo Nogueira (1)

1 I2M - Institut de Mathématiques de Marseille

We study the long-term behavior of injective piecewise contractions of the interval. We prove that every injective piecewise contraction with n − 1 discontinuities has at most n periodic orbits and is topologically conjugate to a piecewise linear contraction.

Domaines: Systèmes dynamiques [math.DS]

Arnaldo Nogueira. Dynamics of piecewise contractions of the interval. Ergodic Theory and Dynamical Systems, 2015, 35 (07), pp.2198-2215. ⟨10.1017/etds.2014.16⟩. ⟨hal-01268227⟩