Authors
Evelyn Sander, James A Yorke
Publication date
2009/4
Journal
Ergodic Theory and Dynamical Systems
Volume
29
Issue
2
Pages
715-731
Publisher
Cambridge University Press
Description
A discontinuous change in the size of an attractor is the most easily observed type of global bifurcation. More generally, an explosion is a discontinuous change in the set of recurrent points. An explosion often results from heteroclinic and homoclinic tangency bifurcations. We prove that, for one-dimensional maps, explosions are generically the result of either tangency or saddle-node bifurcations. Furthermore, we give necessary and sufficient conditions for generic tangency bifurcations to lead to explosions.
Total citations
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Scholar articles
E Sander, JA Yorke - Ergodic Theory and Dynamical Systems, 2009