On weighted sub-additive topological and measure-theoretic pressures

Abstract

Based on several types of weighted sub-additive topological pressures which arise from the theory of Carathéodory structure, we define various weighted sub-additive measure-theoretic pressures. Also, a characterization of weighted sub-additive measure-theoretic pressures for ergodic measures is derived in terms of weighted measure-theoretic entropy, which immediately indicates an inverse variational principle for weighted sub-additive topological pressure. Afterward we illustrate that the inverse variational principle can be attained on the set of generic points of the ergodic measure μ when the potential is additive.

Keywords:

• Weighted topological pressure
• weighted measure-theoretic pressure
• sub-additive potentials
• generic points
• ergodic measures

2010 Mathematics Subject Classifications:

• 37A35
• 37B40
• 37C45

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China (Grant No. 12001192).