The statistical stability of equilibrium states for interval maps

Michael John Todd, Jorge Freitas

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

We consider families of transitive multimodal interval maps with polynomial growth of the derivative along the critical orbits. For these maps Bruin and Todd have shown the existence and uniqueness of equilibrium states for the potential phivt : x map −t log |Df(x)|, for t close to 1. We show that these equilibrium states vary continuously in the weak* topology within such families. Moreover, in the case t = 1, when the equilibrium states are absolutely continuous with respect to Lebesgue, we show that the densities vary continuously within these families.
Original languageEnglish
Pages (from-to)259-281
JournalNonlinearity
Volume22
Issue number2
DOIs
Publication statusPublished - Feb 2009

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