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The splitting of separatrices for analytic diffeomorphisms

Published online by Cambridge University Press:  19 September 2008

E. Fontich  and
C. Simó
E. Fontich
Affiliation:
Dept. de Matemàtica Aplicada, E.T.S.E.I.B., University Politècnica de Catalunya, Barcelona, Spain
C. Simó
Affiliation:
Dept. de Matemàtica Aplicada i Anàlisi, University de Barcelona, Barcelona, Spain
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Abstract

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We study families of diffeomorphisms close to the identity, which tend to it when the parameter goes to zero, and having homoclinic points. We consider the analytical case and we find that the maximum separation between the invariant manifolds, in a given region, is exponentially small with respect to the parameter. The exponent is related to the complex singularities of a flow which is taken as an unperturbed problem. Finally several examples are given.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 2 , June 1990 , pp. 295 - 318
Copyright
Copyright © Cambridge University Press 1990

References

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