Continuity of entropy for Lorenz maps

Zoe Cooperband, Erin Pearse, Blaine Quackenbush, Jordan Rowley, Tony Samuel, Matt West

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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).
Original languageEnglish
Pages (from-to)96-105
Number of pages10
JournalIndagationes Mathematicae
Issue number1
Early online date2 Nov 2019
Publication statusPublished - Jan 2020


  • Kneading sequences
  • Interval maps
  • Topological entropy
  • Matching


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