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Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes

Published online by Cambridge University Press:  01 April 2009

L. J. DÍAZ ,
V. HORITA ,
I. RIOS  and
M. SAMBARINO
L. J. DÍAZ
Affiliation:
DMAT, PUC-Rio, R. Marquês de S. Vicente 225, 22453-900 Rio de Janeiro RJ, Brazil (email: lodiaz@mat.puc-rio.br)
V. HORITA
Affiliation:
Universidade Estadual Paulista (UNESP), IBILCE, Rua Cristóvão Colombo 2265, 15054-000 S. J. Rio Preto SP, Brazil (email: vhorita@ibilce.unesp.br)
I. RIOS
Affiliation:
IM-Universidade Federal Fluminense, Rua Mário de Santos Braga, s/n, 24020-140 Niterói RJ, Brazil (email: isabel@mat.uff.br)
M. SAMBARINO
Affiliation:
Centro de Matemática - Facultad de Ciencias, Univ. de la República, C. Iguá 4225, 11400 Montevideo, Uruguay (email: samba@cmat.edu.uy)
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Abstract

In this paper, we propose a model for the destruction of three-dimensional horseshoes via heterodimensional cycles. This model yields some new dynamical features. Among other things, it provides examples of homoclinic classes properly contained in other classes and it is a model of a new sort of heteroclinic bifurcations we call generating.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 2 , April 2009 , pp. 433 - 474
Copyright
Copyright © Cambridge University Press 2008

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