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August  2007, 17(3): 589-627. doi: 10.3934/dcds.2007.17.589

How do hyperbolic homoclinic classes collide at heterodimensional cycles?

Lorenzo J. Díaz 1, and  Jorge Rocha 2,

1. 

Dep. Matemática PUC-Rio, Marquês de São Vicente 225 22453-900, Rio de Janeiro, Brazil
2. 

Departamento de Matemática Pura, Universidade do Porto, Rua do Campo Alegre, 687,4169-007 Porto, Portugal

Received  February 2006 Revised  September 2006 Published  December 2006

We present a model illustrating heterodimensional cycles (i.e., cycles associated to saddles having different indices) as a mechanism leading to the collision of hyperbolic homoclinic classes (of points of different indices) and thereafter to the persistence of (heterodimensional) cycles. The collisions are associated to secondary (saddle-node) bifurcations appearing in the unfolding of the initial cycle.
Keywords: thickness of a Cantor set., homoclinic class, saddle-node bifurcation, heterodimensional cycle, partial hyperbolicity.
Mathematics Subject Classification: Primary: MSC 2000: 37G25, 37G30, 37D3.
Citation: Lorenzo J. Díaz, Jorge Rocha. How do hyperbolic homoclinic classes collide at heterodimensional cycles?. Discrete & Continuous Dynamical Systems - A, 2007, 17 (3) : 589-627. doi: 10.3934/dcds.2007.17.589
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