Ergodic properties of Viana-like maps with singularities in the base dynamics

Jose Ferreira Alves (1) , Daniel Schnellmann (2)

1 Universidade do Porto = University of Porto
2 DMA - Département de Mathématiques et Applications - ENS Paris

We consider two examples of Viana maps for which the base dynamics has singularities (discontinuities or critical points) and show the existence of a unique absolutely continuous invariant probability measure and related ergodic properties such as stretched exponential decay of correlations and stretched exponential large deviations.

Mots clés: Almost Sure Invariance Principle; Berry-Esseen Theorem; Central Limit Theorem; Decay of Correlations; Large Deviations; Local Limit Theorem; Viana maps

Domaines: Systèmes dynamiques [math.DS]

Jose Ferreira Alves, Daniel Schnellmann. Ergodic properties of Viana-like maps with singularities in the base dynamics. 2011. ⟨hal-00619095⟩