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Abstract
Let $f$ be a real-valued function defined on the phase space of a
dynamical system. Ergodic optimization is the study of those orbits,
or invariant probability measures, whose ergodic $f$-average is as
large as possible.
In these notes we establish some basic aspects of the theory:
equivalent definitions of the maximum ergodic average, existence and
generic uniqueness of maximizing measures, and the fact that every
ergodic measure is the unique maximizing measure for some continuous
function. Generic properties of the support of maximizing measures
are described in the case where the dynamics is hyperbolic. A
number of problems are formulated.
Mathematics Subject Classification: Primary: 37D20; Secondary: 37A05, 37D35, 37E10.
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