Hostname: page-component-5c6d5d7d68-sv6ng Total loading time: 0 Render date: 2024-08-16T01:04:28.110Z Has data issue: false hasContentIssue false
  • English
  • Français

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

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

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.)