TY - JOUR

T1 - Statistical stability for equilibrium states

AU - Freitas, Jorge Milhazes

AU - Todd, Mike

PY - 2011

Y1 - 2011

N2 - We consider multimodal interval maps with at least polynomial growth of the derivative along the critical orbit. For these maps Bruin and Todd showed the existence and uniqueness of equilibrium states for the potential φ{symbol}t: x →tlog{pipe}Df(x){pipe}, for t close to 1. We show that for certain families of this type of maps the equilibrium states vary continuously in the weak* topology, when we perturb the map within the respective family. Moreover, in the case t D 1, when the equilibrium states are absolutely continuous with respect to Lebesgue, we show that the densities also vary continuously in the L1-norm.

AB - We consider multimodal interval maps with at least polynomial growth of the derivative along the critical orbit. For these maps Bruin and Todd showed the existence and uniqueness of equilibrium states for the potential φ{symbol}t: x →tlog{pipe}Df(x){pipe}, for t close to 1. We show that for certain families of this type of maps the equilibrium states vary continuously in the weak* topology, when we perturb the map within the respective family. Moreover, in the case t D 1, when the equilibrium states are absolutely continuous with respect to Lebesgue, we show that the densities also vary continuously in the L1-norm.

UR - http://www.scopus.com/inward/record.url?scp=84904126229&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-14788-3_24

DO - 10.1007/978-3-642-14788-3_24

M3 - Article

AN - SCOPUS:84904126229

SN - 2190-5614

VL - 2

SP - 317

EP - 321

JO - Springer Proceedings in Mathematics

JF - Springer Proceedings in Mathematics

ER -