Let T:X→X be a continuous map and let f:X→R be a continuous function. A T-invariant probability measure m is called f-optimal if the integral of f with respect to m is larger than the integral of f with respect to any other T-invariant probability measure. When the space X is compact and f has some regularity, several techniques have been developed in order to find and describe optimal measures (see [1]). There are several difficulties when trying to extend these results to the non-compact case (X non-compact). In [2] the authors overcome those difficulties under certain assumptions on the system and on the function f. In this talk we will discuss some results from [1] and [2].

[1]	Jenkinson, O. Geometric Barycenters of invariant measures for circle maps ETDS 21 (2001).
[2]	Jenkinson, O., Mauldin, D., Urbanski, M. Ergodic optimization for non-compact dynamical systems (2003)