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On stochastic stability of intermittent circle maps

Sebastian van Strien
Imperial College London

Ergodic Theory and Dynamical Systems

Organisers: Andrew Ferguson, Thomas Jordan

ABSTRACT
It is well-known that the Manneville-Pomeau map with a parabolic fixed point of the form x -> x+x^{1+t} is stochastically stable for t greater than or equal to 1 and converges weakly to the Dirac measure at the fixed point. In this paper we show that if 0<t<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.