Differentiability Properties of the Pre-Image Pressure

We study the differentiability properties of the pre-image pressure. For a TDS (X,T) with finite topological pre-image entropy, we prove the pre-image pressure function Ppre(T,•) is Gateaux differentiable at f∈C(X,R) if and only if Ppre(T,•) has a unique tangent functional at f. Also, we obtain some...

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Main Authors: Kesong Yan, Fanping Zeng, Gengrong Zhang
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2012/951691
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author Kesong Yan
Fanping Zeng
Gengrong Zhang
author_facet Kesong Yan
Fanping Zeng
Gengrong Zhang
author_sort Kesong Yan
collection DOAJ
description We study the differentiability properties of the pre-image pressure. For a TDS (X,T) with finite topological pre-image entropy, we prove the pre-image pressure function Ppre(T,•) is Gateaux differentiable at f∈C(X,R) if and only if Ppre(T,•) has a unique tangent functional at f. Also, we obtain some equivalent conditions for Ppre(T,•) to be Fréchet differentiable at f.
format Article
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institution Kabale University
issn 1026-0226
1607-887X
language English
publishDate 2012-01-01
publisher Wiley
record_format Article
series Discrete Dynamics in Nature and Society
spelling doaj-art-36dbbb0de35b40879017a28361d310162025-08-20T03:55:02ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/951691951691Differentiability Properties of the Pre-Image PressureKesong Yan0Fanping Zeng1Gengrong Zhang2Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, ChinaDepartment of Mathematics and Computer Science, Liuzhou Teachers College, Liuzhou, Guangxi 545004, ChinaInstitute of Mathematics, Guangxi University, Nanning, Guangxi 530004, ChinaWe study the differentiability properties of the pre-image pressure. For a TDS (X,T) with finite topological pre-image entropy, we prove the pre-image pressure function Ppre(T,•) is Gateaux differentiable at f∈C(X,R) if and only if Ppre(T,•) has a unique tangent functional at f. Also, we obtain some equivalent conditions for Ppre(T,•) to be Fréchet differentiable at f.http://dx.doi.org/10.1155/2012/951691
spellingShingle Kesong Yan
Fanping Zeng
Gengrong Zhang
Differentiability Properties of the Pre-Image Pressure
Discrete Dynamics in Nature and Society
title Differentiability Properties of the Pre-Image Pressure
title_full Differentiability Properties of the Pre-Image Pressure
title_fullStr Differentiability Properties of the Pre-Image Pressure
title_full_unstemmed Differentiability Properties of the Pre-Image Pressure
title_short Differentiability Properties of the Pre-Image Pressure
title_sort differentiability properties of the pre image pressure
url http://dx.doi.org/10.1155/2012/951691
work_keys_str_mv AT kesongyan differentiabilitypropertiesofthepreimagepressure
AT fanpingzeng differentiabilitypropertiesofthepreimagepressure
AT gengrongzhang differentiabilitypropertiesofthepreimagepressure