Lifting factor maps to resolving maps |
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Authors: | Email author" target="_blank">Ian?F?PutnamEmail author |
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Institution: | (1) Department of Mathematics and Statistics, University of Victoria, V8W 3P4 Victoria, B.C., Canada |
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Abstract: | We consider Smale spaces, that is, homeomorphisms of a compact metric spaces possessing canonical coordinates of contracting
(stable) and expanding (unstable) directions. Examples of such dynamical systems include the basic sets for Smale's Axiom
A systems. We also assume that each point of the space is non-wandering and that there is a dense orbit. We show that any
almost one-to-one factor map between two such systems may be lifted in a certain sense to a factor map which is injective
on the local stable sets (i.e., s-resolving). We derive several corollaries. One is a refinement of Bowen's result that every
irreducible Smale space is a factor of an irreducible shift of finite type by an almost one-to-one factor map. We are able
to show that there exists such a factor which is the composition of an s-resolving map and a u-resolving map.
Supported in part by a grant from NSERC, Canada. |
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Keywords: | |
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