Ergodic invariant probability measures and entire functions (Q1307365)

The concept of invariant measures plays a fundamental role in ergodic theory and in the theory of dynamical systems. In this work a family of ergodic invariant non-discrete probability measures will be constructed for non-linear entire functions. To a given relatively open non-empty subset \(U\) of the Julia set of an entire function \(f\) an invariant probability will be constructed whose support intersects \(U\) in a non-empty set.