Differentiability Properties of the Pre-Image Pressure

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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Veröffentlicht in:Discrete dynamics in nature and society 2012, Vol.2012 (2012), p.1-14
Hauptverfasser: Yan, Kesong, Zeng, Fanping, Zhang, Gengrong
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1026-0226
1607-887X