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
μφ is infinite.
Under assumptions of good
inducing schemes, we give conditions under which the
pressure of f for
a perturbed potential φ + sψ
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
μφ + 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.