Resume Leplaideur2010

Renaud Leplaideur:

titre =About equilibirum states at temperature zero.

Résumé =
The study of ergodic optimization is relatively new (about 10 years ago). It is of course more developed for the uniformly hyperbolic settings than for the non-uniformly one, because the notion of equilibrium state is better understand in that first case.
I will recall that this study is related to the fact that the pressure for a potential $\beta\varphi$ has an asymptote as $\beta$ goes to $+\infty$.
Hence, the questions we are interested in are :
1/ What happen to the (unique ?) equilibrium state as $\beta$ goes to $+\infty$ ?
2/ Can the pressure touch the asymptote before $+\infty$ (hence before temperature zero) ?
I shall present some results answering to these questions in both setting (uniformly or non-uniformly) hyperbolic.

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