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Equilibrium states for non-uniformly expanding maps with critical sets

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 Added by Eduardo Santana
 Publication date 2020
  fields
and research's language is English




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In the context of non-uniformly expanding maps, possibly with the presence of a critical set, we prove the existence of finitely many ergodic equilibrium states for hyperbolic potentials. Moreover, the equilibrium states are expanding measures. The technique consists in using an inducing scheme in a finite Markov structure with infinitely many symbols to code the dynamics to obtain an equilibrium state for the associated symbolic dynamics and then projecting it to obtain an equilibrium state for the original map.



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