September  2008, 10(2&3, September): 719-731. doi: 10.3934/dcdsb.2008.10.719

Dynamics and bifurcations of random circle diffeomorphism

1. 

KdV Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018TV Amsterdam, Netherlands, Netherlands

Received  October 2006 Revised  November 2007 Published  June 2008

We discuss iterates of random circle diffeomorphisms with identically distributed noise, where the noise is bounded and absolutely continuous. Using arguments of B. Deroin, V.A. Kleptsyn and A. Navas, we provide precise conditions under which random attracting fixed points or random attracting periodic orbits exist. Bifurcations leading to an explosion of the support of a stationary measure from a union of intervals to the circle are treated. We show that this typically involves a transition from a unique random attracting periodic orbit to a unique random attracting fixed point.
Citation: Hicham Zmarrou, Ale Jan Homburg. Dynamics and bifurcations of random circle diffeomorphism. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 719-731. doi: 10.3934/dcdsb.2008.10.719
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