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Elliptic isles in families of area-preserving maps

Published online by Cambridge University Press:  15 September 2008

P. DUARTE
P. DUARTE*
Affiliation:
CMAF, Faculdade de Ciências da Universidade de Lisboa, Portugal (email: pduarte@ptmat.fc.ul.pt)
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Abstract

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We prove that every one-parameter family of area-preserving maps unfolding a homoclinic tangency has a sequence of parameter intervals, approaching the bifurcation parameter, where the dynamics exhibits wild hyperbolic sets accumulated by elliptic isles. This is a parametric conservative analogue of a famous theorem of Newhouse on the abundance of wild hyperbolic sets.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 6 , December 2008 , pp. 1781 - 1813
Copyright
Copyright © 2008 Cambridge University Press

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