Concavity implies attraction

Jeudi 24 novembre 2011 14:00-15:00 - Michal Misiurewicz - Indianapolis

Résumé : We consider a skew product with the interval $[0,a]$ as a fiber spaceand maps in fibers that are concave and fix $0$. If the map in the baseis an irrational rotation of a circle, then it has been known thatunder some additional conditions there exists a Strange NonchaoticAttractor (SNA) for the system. The proofs involved Lyapunov exponentsand Ergodic Theorem. We show that the existence of an attractorbasically follows only from the uniform concavity of the maps in thefibers. In particular, it does not depend on the map in the base, soit occurs also in a nonautonomous case. Next, we discuss the possiblegeneralizations of the notion of a SNA and show the problems that canoccur in the case when the map in the base is noninvertible.This is a joint work with Lluis Alseda.

Lieu : bât. 425 - 121-123

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