Continuity of entropy for Lorenz maps

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

doi:10.1016/j.indag.2019.10.002

Continuity of entropy for Lorenz maps

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

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let (T_p)_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(T_p) of T_p 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(T_p).

Original language	English
Pages (from-to)	96-105
Number of pages	10
Journal	Indagationes Mathematicae
Volume	31
Issue number	1
Early online date	2 Nov 2019
DOIs	https://doi.org/10.1016/j.indag.2019.10.002
Publication status	Published - Jan 2020

Keywords

Kneading sequences
Interval maps
Topological entropy
Matching

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title = "Continuity of entropy for Lorenz maps",

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).",

keywords = "Kneading sequences, Interval maps, Topological entropy, Matching",

author = "Zoe Cooperband and Erin Pearse and Blaine Quackenbush and Jordan Rowley and Tony Samuel and Matt West",

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T1 - Continuity of entropy for Lorenz maps

AU - Cooperband, Zoe

AU - Pearse, Erin

AU - Quackenbush, Blaine

AU - Rowley, Jordan

AU - Samuel, Tony

AU - West, Matt

PY - 2020/1

Y1 - 2020/1

N2 - 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).

AB - 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).

KW - Kneading sequences

KW - Interval maps

KW - Topological entropy

KW - Matching

UR - https://arxiv.org/abs/1803.04511

U2 - 10.1016/j.indag.2019.10.002

DO - 10.1016/j.indag.2019.10.002

M3 - Article

SN - 0019-3577

VL - 31

SP - 96

EP - 105

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 1

ER -

Continuity of entropy for Lorenz maps

Abstract

Keywords

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