Non-expansive derived horseshoes

Kazuhiro Sakai
Department of Mathematics
Kanagawa University
Yokohama 221-8686
Japan
e-mail: kazsaka@cc.kanagawa-u.ac.jp

Abstract:

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.

PDF file size:

© Copyright 1998, Australian Mathematical Society