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Explosions: global bifurcations at heteroclinic tangencies

Published online by Cambridge University Press:  06 August 2002

K. ALLIGOOD ,
E. SANDER  and
J. YORKE
K. ALLIGOOD
Affiliation:
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA (e-mail: alligood@gmu.edu, esander@gmu.edu)
E. SANDER
Affiliation:
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA (e-mail: alligood@gmu.edu, esander@gmu.edu)
J. YORKE
Affiliation:
Institute for Physical Sciences and Technology, Department of Mathematics and Department of Physics, University of Maryland, College Park, MD 20742, USA (e-mail: yorke@ipst.umd.edu)
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Abstract

We investigate bifurcations in the chain recurrent set for a particular class of one-parameter families of diffeomorphisms in the plane. We give necessary and sufficient conditions for a discontinuous change in the chain recurrent set to occur at a point of heteroclinic tangency. These are also necessary and sufficient conditions for an \Omega-explosion to occur at that point.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 4 , August 2002 , pp. 953 - 972
Copyright
© 2002 Cambridge University Press

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