# MUIC Math

Mathematics at MUIC

### Internal

seminar:oleg_nonlin_seq

# Periodic Nonlinear Dynamics of Sequences

Oleg Evnin
Particle Physics Research Laboratory, Chulalongkorn University

16:00 Wednesday, 12 July 2017, Room 3306, MUIC

### Abstract

I'll give a brief account of Hamiltonian dynamical systems whose degrees of freedom are given by a complex-valued sequence $\alpha_n(t)$, and the Hamiltonian is a quartic combination of $\alpha_n$ and its complex conjugate. Such systems arise naturally as weakly nonlinear approximations to a few interesting equations of mathematical physics, whose linearized perturbations possess a perfectly resonant spectrum of frequencies. A few such equations for sequences display remarkably simple solutions with |$\alpha_n$| being an exactly periodic function of time, while the generating function made of $\alpha_n$ has a simple meromorphic structure in the complex plane. Only the simplest of the equations in this class (the cubic Szego equation) has been thoroughly studied by mathematicians over the course of the last 8 years. The results of that study hint at many more surprising structures waiting to be uncovered for other such systems displaying periodic behaviors.