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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |