Dalia Terhesiu (University of Exeter):
The Pressure Function for Infinite Equilibrium Measures

Abstract:

Assume that (*X*,*f*) is a dynamical system
and that φ
is a real non negative potential such
that the corresponding
*f*-invariant measure
μ_{φ} is infinite.
Under assumptions of good
inducing schemes, we give conditions under which the
pressure of *f* for
a perturbed potential φ + *s*ψ
relates to the pressure of the induced
system.
This extends some of Sarig’s results to the
setting of infinite ‘equilibrium states’.
In addition, limit properties of the family of measures
μ_{φ + sψ}
as *s*→0
are studied and statistical properties
(e.g. correlation coefficients) under the
limit measure are derived.
I will discuss several examples.
This is based on joint work with H. Bruin and M. Todd.