For more information about this meeting, contact 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|
|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
|Date:||09 / 08 / 2008|
|Time:||03:30pm - 05:30pm|