Tangent bundles to regular basic sets in hyperbolic dynamics
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Abstract:
Given a locally maximal compact invariant hyperbolic set $\Lambda$ for a $C^2$ flow or diffeomorphism on a Riemann manifold with $C^1$ stable laminations, we construct an invariant continuous bundle of tangent vectors to local unstable manifolds that locally approximates $\Lambda$ in a certain way.References
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Additional Information
- Luchezar Stoyanov
- Affiliation: School of Mathematics, University of Western Australia, Crawley, WA 6009, Australia
- MR Author ID: 167870
- Email: stoyanov@maths.uwa.edu.au
- Received by editor(s): July 28, 2010
- Received by editor(s) in revised form: November 27, 2010, and January 10, 2011
- Published electronically: August 18, 2011
- Additional Notes: The author thanks the referee for useful comments and suggestions.
- Communicated by: Bryna Kra
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 1623-1631
- MSC (2010): Primary 37D20, 37D40
- DOI: https://doi.org/10.1090/S0002-9939-2011-11001-3
- MathSciNet review: 2869147