The variational principle of topological r-pressure for amenable group actions

Abstract

In this paper, we introduce the notions of the topological r-pressure and measure-theoretic r-pressure for countable discrete amenable group actions. In addition, we establish a variational principle between topological r-pressure and measure-theoretic r-pressure.

Keywords:

• Topological r-pressures
• measure-theoretic r-pressure
• amenable group action
• variational principle

2010 Mathematics Subject Classifications:

• 37A35
• 37B40

Disclosure statement

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

Additional information

Funding

R. Zhang was supported by NNSF of China (12031019).