Constant Slope Maps and the Vere-Jones Classification

We study continuous countably-piecewise monotone interval maps and formulate conditions under which these are conjugate to maps of constant slope, particularly when this slope is given by the topological entropy of the map. We confine our investigation to the Markov case and phrase our conditions in...

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Bibliographic Details
Main Authors:	Jozef Bobok, Henk Bruin
Format:	Article
Language:	English
Published:	MDPI AG 2016-06-01
Series:	Entropy
Subjects:	interval map topological entropy conjugacy constant slope
Online Access:	http://www.mdpi.com/1099-4300/18/6/234

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spelling	doaj-6a77aa442a764964a742af756ac6df672020-11-24T23:18:47ZengMDPI AGEntropy1099-43002016-06-0118623410.3390/e18060234e18060234Constant Slope Maps and the Vere-Jones ClassificationJozef Bobok0Henk Bruin1Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 16629 Praha 6, Czech RepublicFaculty of Mathematics, University of Vienna, Oskar Morgensternplatz 1, 1090 Wien, AustriaWe study continuous countably-piecewise monotone interval maps and formulate conditions under which these are conjugate to maps of constant slope, particularly when this slope is given by the topological entropy of the map. We confine our investigation to the Markov case and phrase our conditions in the terminology of the Vere-Jones classification of infinite matrices.http://www.mdpi.com/1099-4300/18/6/234interval maptopological entropyconjugacyconstant slope
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jozef Bobok Henk Bruin
spellingShingle	Jozef Bobok Henk Bruin Constant Slope Maps and the Vere-Jones Classification Entropy interval map topological entropy conjugacy constant slope
author_facet	Jozef Bobok Henk Bruin
author_sort	Jozef Bobok
title	Constant Slope Maps and the Vere-Jones Classification
title_short	Constant Slope Maps and the Vere-Jones Classification
title_full	Constant Slope Maps and the Vere-Jones Classification
title_fullStr	Constant Slope Maps and the Vere-Jones Classification
title_full_unstemmed	Constant Slope Maps and the Vere-Jones Classification
title_sort	constant slope maps and the vere-jones classification
publisher	MDPI AG
series	Entropy
issn	1099-4300
publishDate	2016-06-01
description	We study continuous countably-piecewise monotone interval maps and formulate conditions under which these are conjugate to maps of constant slope, particularly when this slope is given by the topological entropy of the map. We confine our investigation to the Markov case and phrase our conditions in the terminology of the Vere-Jones classification of infinite matrices.
topic	interval map topological entropy conjugacy constant slope
url	http://www.mdpi.com/1099-4300/18/6/234
work_keys_str_mv	AT jozefbobok constantslopemapsandtheverejonesclassification AT henkbruin constantslopemapsandtheverejonesclassification
_version_	1725580056364843008

Constant Slope Maps and the Vere-Jones Classification

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