Constrained ergodic optimization for generic continuous functions

Abstract

One of the fundamental results of ergodic optimization asserts that for any dynamical system on a compact metric space with the specification property and for a generic continuous function f every invariant probability measure that maximizes the space average of f must have zero entropy. We establish the analogical result in the context of constrained ergodic optimization, which is introduced by [Garibaldi and Lopes, Functions for relative maximization, Dyn. Syst. 22(4) (2007), pp. 511-528].

Keywords:

• Ergodic optimization
• symbolic dynamics
• rotation numbers
• vectors

2010:

• Primary 37E45
• 37B10
• 37A99

Disclosure statement

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

Data availability statement

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

Additional information

Funding

The first author was partially supported by JSPS KAKENHI [grant number 22H01138] and the second author was partially supported by JSPS KAKENHI [grant number 21K13816].