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Non-expansive derived horseshoes

Part of: Connections with other structures, applications Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  09 April 2009

Kazuhiro Sakai
Kazuhiro Sakai
Affiliation:
Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan e-mail: [email protected]
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Abstract

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For a two parameter family of C3 diffeomorphisms having a homoclinic orbit of tangency derived from a horseshoe, the relationship between the measure of the parameter values at which the diffeomorphism (restricted to a certain compact invariant set containing the horseshoe) is not expansive and the Hausdorff dimension of the horseshoe associated to the homoclinic orbit of tangency is investigated. This is a simple application of the Newhouse-Palis-Takens-Yoccoz theory.

Keywords

expansiveHénon maphorseshoeHausdorff dimensionmeasurethicknesshomoclinic orbit of tangency

MSC classification

Secondary: 54H20: Topological dynamics 11K55: Metric theory of other algorithms and expansions; measure and Hausdorff dimension
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 3 , December 1998 , pp. 405 - 415
Copyright
Copyright © Australian Mathematical Society 1998

References

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