On stochastic stability of expanding circle maps with neutral fixed points

Abstract

It is well-known that the Manneville-Pomeau map with a parabolic fixed point of the form $x\mapsto x+x^{1+\alpha }\mathrm{mod}1$ is stochastically stable for $\alpha \ge 1$ and the limiting measure is the Dirac measure at the fixed point. In this paper we show that if $\alpha \in (0,1)$ then it is also stochastically stable. Indeed, the stationary measure of the random map converges strongly to the absolutely continuous invariant measure for the deterministic system as the noise tends to zero.

25 pages

References in corpus (5)

• Strong statistical stability of non-uniformly expanding maps
• Stochastic stability at the boundary of expanding maps
• On stochastic stability of non-uniformly expanding interval maps
• Statistical properties of one-dimensional maps under weak hyperbolicity assumptions
• Strong stochastic stability for non-uniformly expanding maps

Cited by in corpus (1)

• Adapted random perturbations for non-uniformly expanding maps