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Smale spaces with totally disconnected local stable sets

A Smale space is a chaotic dynamical system with canonical coordinates of contracting and expanding directions. The basic sets for Smale’s Axiom A systems are a key class of examples. R.F. Williams considered the special case where the basic set had a totally disconnected contracting set and a Euclidean expanding one. He provided a construction using inverse limits of such examples and also proved that (under appropriate hyptotheses) all such basic sets arose from this construction. We will be working in the metric setting of Smale spaces, but the goal is to extend Williams’ results by removing all hypotheses on the unstable sets. We give criteria on a stationary inverse limit which ensures the result is a Smale space. We also prove that any irreducible Smale space with totally disconnected local stable sets is obtained through this construction. / Graduate

Identiferoai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/3905
Date25 April 2012
CreatorsWieler, Susana
ContributorsPutnam, Ian Fraser
Source SetsUniversity of Victoria
LanguageEnglish, English
Detected LanguageEnglish
TypeThesis
RightsAvailable to the World Wide Web

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