Constrained ergodic optimization for asymptotically additive potentials.

Abstract Using an asymptotically additive sequence of continuous functions as a constrained condition, this paper studies the relations of several constrained ergodic averages for asymptotically additive potentials. Basic properties of constrained maximum ergodic averages are studied. In particular, if the dynamical systems satisfy the specification property, the maximal growth rate of an asymptotically additive potential on the level sets is equal to its constrained maximum ergodic averages and the maximal growth rates on the irregular sets is its unconstrained maximum ergodic averages. Finally, the applications for suspension flows are given in the end of the paper. [ABSTRACT FROM AUTHOR]