Topology Seminar

Wednesday, November 30, 2016
4:20 PM - 5:30 PM (ET)
Exley Science Center Tower ESC 121
Event Type
Canalia, Caryn

Boris Gutkin, University Duisberg-Essen: Pairings between periodic orbits in hyperbolic coupled map lattices.

Abstract: Upon quantization, hyperbolic Hamiltonian systems generically exhibit universal spectral properties effectively described by Random Matrix Theory. Semiclassically this remarkable phenomenon can be attributed to the existence of pairs of classical periodic orbits with small action differences. So far, however, the scope of this theory has, by and large, been restricted to small-dimensional systems. I will discuss an extension of this program to hyperbolic coupled map lattices with a very large number of sites. The crucial ingredient is a two-dimensional symbolic dynamics which allows an effective representation of periodic orbits and their pairings. I will illustrate the theory with a specific model of coupled cat maps, where such a symbolic dynamics can be constructed explicitly.


The core  of the talk is  based on the  joint work with V. Osipov: Nonlinearity  29, 325 (2016) and a   work in progress  with P. Cvitanovic, R. Jafari, L. Han, A. Saremi.


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