Mixing properties in expanding Lorenz maps
type: Item
instance of: scholarly article
title: Mixing properties in expanding Lorenz maps
zbMATH Open document ID: 1416.37040
author: Paweł Potorski
author: Peter Raith
author: Piotr Oprocha
published in: Advances in Mathematics
publication date: 2019-01-18T00:00:00Z
review text: In this paper, the authors find sufficient conditions for an expanding Lorenz map $T_f: [0,1] \rightarrow [0,1]$ to be topologically mixing. One of their main results is that every locally eventually onto Lorenz map is mixing. Additionally, they provide an example to show that the converse is false. They also give an example of a renormalizable expanding Lorenz map which is locally eventually onto but not strongly locally eventually onto. At the end of their paper, the authors show which Lorenz maps $T_f$ are mixing when $f(x) = \beta x + \alpha$ with $\beta \ge \sqrt[3]{2}$.
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 37E20
zbMATH DE Number: 7003604
zbMATH Keywords: Lorenz map
zbMATH Keywords: topological transitivity
zbMATH Keywords: topological mixing
zbMATH Keywords: locally eventually onto
zbMATH Keywords: expanding map
zbMATH Keywords: renormalizable map
reviewed by: Steve Pederson
MaRDI profile type: Publication
full work available at URL: j.aim.2018.11.015
OpenAlex ID: W2905529835
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Wikidata QID: Q128760573
DOI: 10.1016/J.AIM.2018.11.015
description: scientific article; zbMATH DE number 7003604