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Period-doubling cascades galore

Published online by Cambridge University Press:  03 June 2011

EVELYN SANDER  and
JAMES A. YORKE
EVELYN SANDER
Affiliation:
Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, USA (email: [email protected])
JAMES A. YORKE
Affiliation:
Department of Mathematics, IPST, and Physics Department, University of Maryland, College Park, MD 20742, USA (email: [email protected])
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Abstract

The appearance of numerous period-doubling cascades is among the most prominent features of parametrized maps, that is, smooth one-parameter families of maps F:ℝ×𝔐→𝔐, where 𝔐 is a smooth locally compact manifold without boundary, typically ℝN. Each cascade has infinitely many period-doubling bifurcations, and it is typical to observe that, whenever there are any cascades, there are infinitely many cascades. We develop a general theory of cascades for generic F.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 4 , August 2011 , pp. 1249 - 1267
Copyright
Copyright © Cambridge University Press 2011

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