DMCA
Hyperbolic sets that are not locally maximal (2006)
| Venue: | Ergod. Th. Dynamic. Systems |
| Citations: | 3 - 3 self |
BibTeX
@ARTICLE{Fisher06hyperbolicsets,
author = {Todd Fisher},
title = {Hyperbolic sets that are not locally maximal},
journal = {Ergod. Th. Dynamic. Systems},
year = {2006}
}
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Abstract
This papers addresses the following topics relating to the structure of hyperbolic sets: First, hyperbolic sets that are not contained in locally maximal hyperbolic sets. Second, the existence of a Markov partition for a hyperbolic set. We construct new examples of hyperbolic sets which are not contained in locally maximal hyperbolic sets. The first example is robust under per-turbations and can be constructed on any compact manifold of dimension greater than one. The second example is robust, topologically transitive, and constructed on a 4-dimensional manifold. The third example is vol-ume preserving and constructed on R4. We show that every hyperbolic set is included in a hyperbolic set with a Markov partition. Additionally, we describe a condition that ensures a hyperbolic set is included in a locally maximal hyperbolic set. 1
