| Hyperbolic Behaviour in Rich families?-Extended Abstract (2002) | |||||||||||||
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| Hyperbolic behaviour rich families Extended Abstract Michael Shub What reporting joint work with Keith Burns Charles Pugh Amie Wilkinson BuPuShWi Jean Pierre Dedieu DeSh and Francois Ledrappier Carles Simo and Amie Wilkinson LSSW Almost all the contents here are taken from these three papers without specific attribution The material may found much expanded form these references and Any errors which may have crept are mine alone Introduction One the major achievements the uniformly hyperbolic theory dynamical systems the work Anosov Sinai Ruelle and Bowen the ergodic theory uniformly hyperbolic systems Anosov proved that smooth volume preserving globally hyperbolic systems are ergodic Sinai Ruelle and Bowen extended this work specifically constructed invariant measures for general uniformly hyperbolic systems now called SRB measures The ergodicity these measures asserts that although particular histories are difficult compute the statistics these histories the probability that point given region given time captured the measure Much the work dynamical systems recent years has been attempt extend the results the uniformly hyperbolic theory more general systems One theme relax the notion uniform hyperbolicity non uniform partial hyperbolicity and then conclude the existence measures sharing ergodic properties the SRB measures The Proceedings the Seattle AMS Summer Symposium Smooth Ergodic Theory and Its Applications contains much along these lines particular you can find the surv | |||||||||||||
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