Poincaré-Melnikov theory for n-dimensional diffeomorphisms

M. Baldomà; E. Fontich

Applicationes Mathematicae (1998)

  • Volume: 25, Issue: 2, page 129-152
  • ISSN: 1233-7234

Abstract

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We consider perturbations of n-dimensional maps having homo-heteroclinic connections of compact normally hyperbolic invariant manifolds. We justify the applicability of the Poincaré-Melnikov method by following a geometric approach. Several examples are included.

How to cite

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Baldomà, M., and Fontich, E.. "Poincaré-Melnikov theory for n-dimensional diffeomorphisms." Applicationes Mathematicae 25.2 (1998): 129-152. <http://eudml.org/doc/219197>.

@article{Baldomà1998,
abstract = {We consider perturbations of n-dimensional maps having homo-heteroclinic connections of compact normally hyperbolic invariant manifolds. We justify the applicability of the Poincaré-Melnikov method by following a geometric approach. Several examples are included.},
author = {Baldomà, M., Fontich, E.},
journal = {Applicationes Mathematicae},
keywords = {Melnikov function; splitting of separatrices; homoclinic solutions; -dimensional maps; Melnikov functions},
language = {eng},
number = {2},
pages = {129-152},
title = {Poincaré-Melnikov theory for n-dimensional diffeomorphisms},
url = {http://eudml.org/doc/219197},
volume = {25},
year = {1998},
}

TY - JOUR
AU - Baldomà, M.
AU - Fontich, E.
TI - Poincaré-Melnikov theory for n-dimensional diffeomorphisms
JO - Applicationes Mathematicae
PY - 1998
VL - 25
IS - 2
SP - 129
EP - 152
AB - We consider perturbations of n-dimensional maps having homo-heteroclinic connections of compact normally hyperbolic invariant manifolds. We justify the applicability of the Poincaré-Melnikov method by following a geometric approach. Several examples are included.
LA - eng
KW - Melnikov function; splitting of separatrices; homoclinic solutions; -dimensional maps; Melnikov functions
UR - http://eudml.org/doc/219197
ER -

References

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  13. [13] H. E. Lomelí, Transversal heteroclinic orbits for perturbed billiards, preprint, 1994. 
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