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April  2006, 14(2): 343-354. doi: 10.3934/dcds.2006.14.343

Heteroclinic orbits and rotation sets for twist maps

Héctor E. Lomelí 1,

1. 

Department of Mathematics, Instituto Tecnológico Autónomo de México, Río Hondo # 1., Tizapán San Angel, México DF 01000, Mexico

Received  November 2004 Revised  May 2005 Published  November 2005

We show how the shadowing property can be used in connection to rotation sets. We review the concept of periodic chains and the shadowing rotation property, and study a class of diffeomorphisms with invariant sets that have such property. In particular, we consider invariant sets that arise from homoclinic and heteroclinic connections for twist maps in higher dimensions. As a consequence, we can show the existence of a family of twist maps, each one with an open set of rotation vectors that are realized by points that are close to a fixed point.
Keywords: heteroclinic orbits, Rotation set, Melnikov method, twist maps, shadowing., Farey.
Mathematics Subject Classification: Primary: 37E45, 37E40 Secondary: 37C50, 37J4.
Citation: Héctor E. Lomelí. Heteroclinic orbits and rotation sets for twist maps. Discrete and Continuous Dynamical Systems, 2006, 14 (2) : 343-354. doi: 10.3934/dcds.2006.14.343
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