Dynamical systems and asymptotic analysis; an age old symbiosis #

Alan Champneys

12:10 Wednesday in 4Q04.

Part of the Nonlinear dynamics and applications session.

Abstract #

This talk will be based on a sneak previous of my next Westward Ho! feature for the IMA’s Mathematics Today magazine. It is based on the story of dynamics in the 19th Century, which then was pretty much synonymous with celestial mechanics. We start with the young John Couch Adams whose asymptotic analysis enabled the discovery of Neptune. We compare and contrast with the work of Henri Poincare who introduced many of the notions we now understand from the geometric theory of dynamical systems in analysing the planar three-body problem. We draw parallels to modern applied mathematics, where both symbolic asymptotic analysis and geometric theory of dynamical systems each have their uses when applied to similar problems.