Induced maps, Markov extensions and invariant measures in one-dimensional dynamics
type: Item
instance of: scholarly article
title: Induced maps, Markov extensions and invariant measures in one-dimensional dynamics
zbMATH Open document ID: 0827.58015
DOI: 10.1007/BF02101844
published in: Communications in Mathematical Physics
publication date: 1995-12-19T00:00:00Z
review text: The paper deals with interval maps \(f : I \to I\) that are piecewise continuous and piecewise monotone. The relation of induced maps \(F\) to \(f\) in the sense that \(F\) coincides on certain subintervals with iterates of \(f\) and the Markov extension of \(f\) is discussed. For the case that \(f\) is a non-flat \(S\)-unimodal map the author gives a simple inequality as a necessary condition for \(f\) to have an absolutely continuous invariant probability measure.
Mathematics Subject Classification ID: 37E99
zbMATH DE Number: 778974
zbMATH Keywords: interval maps
zbMATH Keywords: induced maps
zbMATH Keywords: Markov extension
zbMATH Keywords: invariant probability measure
Wikidata QID: Q59184911
author: Henk Bruin
reviewed by: Hermann Haase
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 778974