Heteroclinic orbits and rotation sets for twist maps

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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

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

Abstract
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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 & Continuous Dynamical Systems - A, 2006, 14 (2) : 343-354. doi: 10.3934/dcds.2006.14.343

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