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Invariant manifolds for near identity differentiable maps and splitting of separatrices

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 consider families of differentiable diffeomorphisms with hyperbolic points, close to the identity, which tend to it when the parameter goes to zero.

We study the asymptotic behaviour of the invariant manifolds. Then we consider the case when there are homo-heteroclinic points and we find that the maximum separation between the invariant manifolds is of the order of some power of the parameter which is related to the degree of differentiability.

Finally the analogous case for flows is considered.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 2 , June 1990 , pp. 319 - 346
Copyright
Copyright © Cambridge University Press 1990

References

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