Differentiable conjugacies for one-dimensional maps

Paul Glendinning, David J. W. Simpson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity. We describe some of the techniques and recent results that allow differentiable conjugacies to be dened for standard bifurcations, and explain how this leads to a new class of normal forms. Closed-form expressions for differentiable conjugacies exist between some chaotic maps, and we describe some of the constraints that make it possible to recognise when such conjugacies arise. This paper focuses on the consequences of the existence of differentiable conjugacies rather than the conjugacy classes themselves.
Original languageEnglish
Title of host publicationAdvances in Discrete Dynamical Systems, Difference Equations and Applications
Subtitle of host publication26th ICDEA, Sarajevo, Bosnia and Herzegovina, July 26-30, 2021
Volume416
Publication statusAccepted/In press - 4 Jun 2023

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer
Volume416
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Keywords

  • differentiable conjugacy
  • bifurcation
  • normal form
  • chaos

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