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Basins of attraction near homoclinic tangencies

Published online by Cambridge University Press:  19 September 2008

J.C. Tatjer
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain
C. Simó
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain

Abstract

We describe the behaviour of the basin of attraction of the attracting periodic points which appear near a non-degenerate tangential homoclinic point of a dissipative saddle fixed point for one-parameter families of planar diffeomorphisms. This behaviour depends on certain relations between the eigenvalues of the saddle point and on the geometry of the tangency.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1994

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