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Diffeomorphisms with infinitely many irrational invariant curves

Published online by Cambridge University Press:  23 November 2010

LEONARDO MORA  and
BLADISMIR RUIZ
LEONARDO MORA
Affiliation:
Departamento de Matemática, Facultad de Ciencias, La Hechicera, Universidad de los Andes, Mérida, 5101, Venezuela (email: lmora@ula.ve, bladismir@ula.ve)
BLADISMIR RUIZ
Affiliation:
Departamento de Matemática, Facultad de Ciencias, La Hechicera, Universidad de los Andes, Mérida, 5101, Venezuela (email: lmora@ula.ve, bladismir@ula.ve)
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Abstract

For a surface diffeomorphism f∈Diff l(M), with l≥8, we prove that if f exhibits a non-transversal heteroclinic cycle composed of two fixed saddle points Q1 and Q2, one dissipative and the other expansive, then there exists an open set 𝒱⊂Diff l(M) such that and there exists a dense set 𝒟⊂𝒱 such that for all g∈𝒟, g exhibits infinitely many invariant periodic curves with irrational rotation numbers. Moreover, these curves are C1 conjugated to an irrational rotation on 𝕊1.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 5 , October 2011 , pp. 1517 - 1535
Copyright
Copyright © Cambridge University Press 2010

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