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).
|Number of pages||10|
|Early online date||2 Nov 2019|
|Publication status||Published - Jan 2020|
- Kneading sequences
- Interval maps
- Topological entropy