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Analysis and PDE Seminar

Date:
-
Location:
745 Patterson Office Tower
Speaker(s) / Presenter(s):
Professor Peter Perry, University of Kentucky

TITLE:  Scattering Resonances on Hyperbolic Manifolds as a Model of Chaotic Scattering

ABSTRACT:  Scattering resonances represent "almost standing waves" in a scattering system which have a nite lifetime as measured by energy decay in a nte region.  In this survey talk well review the basics of scattering theory on geometrically nite, real hyperbolic manifolds and their role as models of open chaotic systems. As such they have attracted the interest of both mathematicians and physicists. Work to be discussed includes the work of Patterson and Perry and papers by Borthwick, Guillope-Zworski, Guillarmou, Naud, and others.  Real hyperbolic manifolds provide a useful "laboratory" for scattering because their symmetries allow for the use of powerful methods from the theory of automorphic functions, dynamics, and the theory of Fuchsian groups. We'll discuss the connection between scattering resonances and Helberg's zeta function for a hyperbolic surface, and in turn the connection between Selberg's zeta function and the Ruelle zeta function from dynamical systems. Through this connection one can uncover close relationships between the Hausdor  dimension of the trapped set for geodesic ow on the one hand, and the distribution of scattering resonances on the other.

Event Series: