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July  2000, 6(3): 691-704. doi: 10.3934/dcds.2000.6.691

Multipliers of homoclinic orbits on surfaces and characteristics of associated invariant sets

V. Afraimovich 1, and  T.R. Young 2,

1. 

IICO-UASLP, A. Obregón 64, 78000 San Luis Postosí, SLP
2. 

Department of Mathematics, Ohio University, Athens, OH 45701, United States

Received  December 1998 Revised  January 2000 Published  April 2000

Suppose that $f$ is a surface diffeomorphism with a hyperbolic fixed point $\mathcal O$ and this fixed point has a transversal homoclinic orbit. It is well known that in a vicinity of this type of homoclinic there are hyperbolic invariants sets. We introduce smooth invariants for the homoclinic orbit which we call the multipliers. As an application, we study the influence of the multipliers on numerical invariants of the hyperbolic invariant sets as the vicinity becomes small.
Keywords: transversal homoclinic., smooth invariant, Hyperbolic set.
Mathematics Subject Classification: 34C35, 58C2.
Citation: V. Afraimovich, T.R. Young. Multipliers of homoclinic orbits on surfaces and characteristics of associated invariant sets. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 691-704. doi: 10.3934/dcds.2000.6.691
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