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Measure Pressure for Measure Preserving Maps and an Upper Bound for the Case of $C^2$ Endomorphisms
Sanaz Lamei
,
Pouya Mehdipour
,
Maryam Razi
Abstract
A measure-theoretic pressure was defined by [L. He, J. Lv and L. Zhou: Definition of measure-theoretic pressure using spanning sets, Acta Math. Sinica (English Series) 20, 709–718 (2004)] based on the Katok entropy formula. For a measure preserving map f, we generalized this definition to define a measure-theoretic pressure by using both $(n,\epsilon )$-spanning and $(n,\epsilon )$-separated sets. A variational principle for this pressure is established. Furthermore, we investigate an upper bound for the measure theoretic pressure of a $C^{2}$ endomorphism preserving a hyperbolic measure.