Solvable N-body Problems and Associated Diophantine Properties

by Oksana Bihun (Department of Mathematics and Computer Science, Concordia College)

Wednesday 15 May 2013, 15:00 → 16:00 Europe/Rome

Aula 7 (Dip. di Fisica - Edificio E. Fermi)

If a solution f(z,t) of a linear PDE is a polynomial in z, i.e. f(z,t)=[z-z_1(t)][z-z_2(t)]...[z-z_N(t)], its time-dependent zeros z_k(t), k=1,2,...,N, satisfy a nonlinear system of differential equations that can be interpreted as an N-body problem. We will discuss a class of solvable N-body problems constructed using this idea. We will formulate the conditions that yield isochronous solutions of this class of systems. The associated diophantine properties of certain matrices constructed using the equilibria of this class of systems will be discussed.