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: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/951691 |
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| _version_ | 1849306564025909248 |
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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 |
| id | doaj-art-36dbbb0de35b40879017a28361d31016 |
| 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 |