| Abstract: |
| The main purpose of the ergodic optimization is to describe invariant measures which maximize the space average of a continuous function on a dynamical system. The generic uniqueness and the low-complexity of maximizing measures are proved by several authors. We prove, on the other hand, there exits a dense subset of continuous functions which have uncountably many ergodic maximizing measures. Moreover in the case of subshift of finite type we can show that the uncountably many measures have positive entropy. The main idea of our proof is the application of the Bishop Phelps theorem to the context of maximizing measures. |
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