Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-25T12:17:30.073Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)