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Basins of attraction near homoclinic tangencies

Published online by Cambridge University Press:  19 September 2008

J.C. Tatjer  and
C. Simó
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
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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
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 2 , June 1994 , pp. 351 - 390
Copyright
Copyright © Cambridge University Press 1994

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