Differentiability Properties of the Pre-Image Pressure. (27th May 2012)

• Record Type: Journal Article
• Authors: Yan, Kesong; Zeng, Fanping; Zhang, Gengrong
• Other Names: De la Sen M. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2012(2012)
• Publication Date: 2012-05-27
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2012/951691
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : 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 P p r e ( T, ) is Gateaux differentiable at f ∈ C ( X, R ) if and only if P p r e ( T, ) has a unique tangent functional at f . Also, we obtain some equivalent conditions for P p r e ( T, ) to be Fréchet differentiable at f .