Statistical stability of equilibrium states for interval maps

Details Statistical stability of equilibrium states for interval maps Statistical stability of equilibrium states for interval maps

2007-09-10

arxiv.org/abs/0709.1395v3

Nonlinearity 22 (2009) 259-281

Mathematics

Dynamical Systems

More details given and the appendices now incorporated into the rest of the paper

Scientific paper

10.1088/0951-7715/22/2/002

We consider families of 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 $\phi_t:x\mapsto-t\log|Df(x)|$, 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.

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