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.