Residual behavior of induced maps
type: Item
instance of: scholarly article
title: Residual behavior of induced maps
zbMATH Open document ID: 0864.28011
DOI: 10.1007/BF02761114
published in: Israel Journal of Mathematics
publication date: 1997-06-24T00:00:00Z
review text: Given a Lebesgue probability space \((X,{\mathcal F}, \mu,T)\) and \(A\in {\mathcal F}\) one can define the induced map \(T_A:A\to A\) by \(T_A(x)= T^{r(x)}(x)\) where \(r(x)= \min \{i>0 \mid T(x)\in A\}\). For ergodic \(T\) and a residual set of \(A\) the authors give a number of results investigating the type of transformation \(T_A\) is. The results depend on the whether the entropy is zero or positive, and whether \(T\) is loosely Bernoulli.
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 878302
zbMATH Keywords: ergodic transformations
zbMATH Keywords: Lebesgue probability space
zbMATH Keywords: residual set
zbMATH Keywords: entropy
zbMATH Keywords: loosely Bernoulli
author: A. Del Junco
author: Daniel J. Rudolph
MaRDI profile type: Publication
cites work: Q5541480
cites work: Equations fonctionnelles et syst�mes induits en th�orie ergodique
cites work: α-equivalence: a refinement of Kakutani equivalence
cites work: Ergodic transformations induce mixing transformations
cites work: Q3234755
cites work: Q3345022
cites work: APPROXIMATIONS IN ERGODIC THEORY
cites work: Equivalence of measure preserving transformations
cites work: Ergodic flows of positive entropy can be time changed to become K-flows
cites work: Q5667036
cites work: Classifying the isometric extensions of a Bernoulli shift
full work available at URL: https://doi.org/10.1007/bf02761114
OpenAlex ID: W2000019652
Recommended article: Induced residuated maps
Recommended article: Residuality of dynamical morphisms
Recommended article: Residuated mappings
Recommended article: On residuated mappings
Recommended article: Some properties of the induced map
Recommended article: Residues for maps generically transverse to distributions
Recommended article: Regularity of residuated mappings
Recommended article: Q5413350
Recommended article: A note on induced mappings
Recommended article: The residual index and the dynamics of holomorphic maps tangent to the identity
description: scientific article; zbMATH DE number 878302