PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Mari Royer, Yakov Pesin, Anatole Katok, Svetlana Katok, Dmitri Burago.

Title:Multifractal analysis for the backward continued fraction map
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Godofredo Iommi, Pontificia Universidad Católica de Chile
Abstract:
In this talk we study the multifractal spectrum of Lyapunov exponents for interval maps with infinitely many branches and a parabolic fixed point. An example of such maps is the backward continued fraction map. It turns out that, in strong contrast with the hyperbolic case, the domain of the spectrum is unbounded and points of non-differentiability might exist. Moreover, the spectrum is not concave. We also study the thermodynamic formalism for such maps. We prove that the pressure function is real analytic in a certain interval and then it becomes equal to zero. We also discuss the existence and uniqueness of equilibrium measures. In order to do so, we introduce a family of countable Markov shifts that can be thought of as a generalisation of the renewal shift.

Room Reservation Information

Room Number:MB106
Date:09 / 08 / 2008
Time:03:30pm - 05:30pm