EVENT DETAILS AND ABSTRACT

Title: Exponential Divergence
Speaker: Douglas Heggie
Speaker Info: University of Edinburgh
Brief Description:
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Abstract:

The famous "butterfly effect" is expressed quantitatively by Liapounov exponents, which measure the rate of divergence of neighbouring solutions of a dynamical system. This lecture begins by reviewing the basic notions of this body of theory, and illustrates these in the context where so much non-linear dynamics was first developed: the N-body problem. The distinction between N=2 and N=3 illustrates the link between the Liapounov exponents and integrability. We illustrate the practical limitations imposed by looking at divergence over a finite time, and in the regime where the divergence can no longer be considered as small, where new results will be presented. Finally we consider the implications of exponential divergence in the realm of computer simulation.