Continuity of entropy for Lorenz maps

Research output: Contribution to journalArticlepeer-review

Authors

  • Zoe Cooperband
  • Erin Pearse
  • Blaine Quackenbush
  • Jordan Rowley
  • Tony Samuel
  • And 1 others
  • Matt West

Colleges, School and Institutes

External organisations

  • UNIVERSITY OF CALIFORNIA IRVINE
  • California Polytechnic State University
  • California Polytechnic State University

Abstract

Let (Tp)p denote a one parameter family of expanding interval maps with two increasing and continuous branches and indexed by their point of discontinuity. Using the pressure formula from thermodynamics, P. Raith (2000) showed that the topological entropy h(Tp) of Tp varies continuously as a function of p. Here we provide a new and alternative proof of this result based on Milnor-Thurston kneading theory, as well as some observations on the monotonicity of p→h(Tp).

Details

Original languageEnglish
Number of pages10
JournalIndagationes Mathematicae
Early online date2 Nov 2019
Publication statusE-pub ahead of print - 2 Nov 2019

Keywords

  • Kneading sequences, Interval maps, Topological entropy, Matching