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Wreath products along the period-doubling route to chaos

Published online by Cambridge University Press:  01 December 1999

J. D. H. SMITH
J. D. H. SMITH
Affiliation:
Department of Mathematics, Iowa State University, Ames, IA 50011, USA
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Abstract

The wreath-product construction is used to give a complete combinatorial description of the dynamics of period-doubling quadratic maps leading to the Feigenbaum map. An explicit description of the action on periodic points uses the Thue–Morse sequence. In particular, a wreath-product construction of this sequence is given. The combinatorial renormalization operator on the period-doubling family of maps is invertible.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 6 , December 1999 , pp. 1617 - 1636
Copyright
1999 Cambridge University Press

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