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Mar 2013

Volume 54, Issue 3, Articles (03xxxx)

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J. Math. Phys. 54, 033512 (2013); http://dx.doi.org/10.1063/1.4794514 (20 pages)

Andrew Neate and Aubrey Truman
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back to top Dynamical Systems

Variational principles for relative local pressure with subadditive potentials

Xianfeng Ma and Ercai Chen

J. Math. Phys. 54, 032701 (2013); http://dx.doi.org/10.1063/1.4794086 (25 pages)

Online Publication Date: 11 March 2013

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We prove two relative local variational principles of topological pressure functions P(T,F,U,y) and P(T,F,U|Y) for a given factor map π: (X, T) → (Y, S) between two topological dynamical systems, an open cover U of X and a subadditive potential F in C(X,math). By proving the upper semi-continuity and affinity of the entropy maps μ→hμ(T,U∣Y) and μ→hμ+(T,U∣Y) on the space of all invariant Borel probability measures, we show that the relative local topological pressure with subadditive potentials determines the local measure-theoretic conditional entropies.
Show PACS
02.30.Xx Calculus of variations
02.40.Re Algebraic topology
02.50.Cw Probability theory
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