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On the generic existence of homoclinic points

Published online by Cambridge University Press:  19 September 2008

Fernando Oliveira
Fernando Oliveira
Affiliation:
Departamento de Matemática, ICEX-UFMG, Caixa Postal 702, 30161-Belo Horizonte-MG, Brazil
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Abstract

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This work is concerned with the generic existence of homoclinic points for area preserving diffeomorphisms of compact orientable surfaces. We give a shorter proof of Pixton's theorem that shows that, Cr-generically, an area preserving diffeomorphism of the two sphere has the property that every hyperbolic periodic point has transverse homoclinic points. Then, we extend Pixton's result to the torus and investigate certain generic aspects of the accumulation of the invariant manifolds all over themselves in the case of symplectic diffeomorphisms of compact manifolds.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 4 , December 1987 , pp. 567 - 595
Copyright
Copyright © Cambridge University Press 1987

References

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