Ergodic optimization theory for Axiom A flows

Abstract

In this article, we consider the weighted ergodic optimization problem Axiom A attractors of a $C^2$ flow on a compact smooth manifold. The main result obtained in this paper is that for a generic observable from function space $\mc C^{0,\a}$ ($\a\in(0,1]$) or $\mc C^1$ the minimizing measure is unique and is supported on a periodic orbit.