The Toda Lattice is a model of particles on the line that interact via an exponential repulsive force. It is known that when the potentials are governed by the root system of a simple Kac-Moody Lie algebra the equations of motion are completely integrable.
This talk will describe a family of Toda-like integrable systems. These systems, like the example of Bolsinov and Taimanov, are notable because they also have positive topological entropy.
Time permitting, I'll also explain how the classification of these dynamical systems up to topological conjugacy leads to an old conjecture in transcendental number theory concerning the algebraic independence of logarithms of algebraic numbers.