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November  2007, 8(4): 971-1005. doi: 10.3934/dcdsb.2007.8.971

Attractors for return maps near homoclinic tangencies of three-dimensional dissipative diffeomorphisms

Antonio Pumariño 1, and  Joan Carles Tatjer 2,

1. 

Departamento de Matemáticas, Universidad de Oviedo, Calvo Sotelo s/n, 33007 Oviedo
2. 

Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08080 Barcelona, Spain

Received  November 2006 Revised  June 2007 Published  August 2007

We numerically analyse different kinds of one-dimensional and two-dimensional attractors for the limit return map associated to the unfolding of homoclinic tangencies for a large class of three-dimensional dissipative diffeomorphisms. Besides describing the topological properties of these attractors, we often numerically compute their Lyapunov exponents in order to clarify where two-dimensional strange attractors can show up in the parameter space. Hence, we are specially interested in the case in which the unstable manifold of the periodic saddle taking part in the homoclinic tangency has dimension two.
Keywords: Lyapunov exponents., Invariant curves, strange attractors.
Mathematics Subject Classification: Primary: 37G35; Secondary: 37C29 37D4.
Citation: Antonio Pumariño, Joan Carles Tatjer. Attractors for return maps near homoclinic tangencies of three-dimensional dissipative diffeomorphisms. Discrete and Continuous Dynamical Systems - B, 2007, 8 (4) : 971-1005. doi: 10.3934/dcdsb.2007.8.971
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