Presentation Name: Non-additive Measure-theoretic Pressure and Applications to Dimensions of an Ergodic Measure
Presenter: Zhao Yun
Date: 2012-03-27
Location: 光华楼东主楼2001室
Abstract:

Without any additional conditions on sub-additive potentials, this paper defines sub-additive measure-theoretic pressure, and shows that the sub-additive measure-theoretic pressure for ergodic measures can be described in terms of measure-theoretic entropy and an constant associated with the ergodic measure. Based on the definition of topological pressure on non-compact set, we give another equivalent definition of sub-additive measure-theoretic pressure, and we can obtain an inverse variational principle. This paper also studies the sup-additive measure-theoretic pressure which has similar formalism as the sub-additive measure-theoretic pressure. Moreover, we prove that the zero of the non-additive measure-theoretic pressure gives the lower and upper bound estimate of dimensions of an ergodic measure.

Annual Speech Directory: No.22

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