The City College of New YorkCCNY
Department of Mathematics
Division of Science

Topological methods in Hamiltonian instability

Mathematics Colloquium

Time and place

1 PM on Thursday, October 18th, 2012; NAC 6/113

Marian Gidea (Institute for Advanced Study)

Abstract

A Hamiltonian system represents a model for the evolution of a physical system. If the system is integrable, then all solutions are rather explicit. A typical Hamiltonian system, however, is non-integrable, exhibiting instability. A paradigm for Hamiltonian instability is the 'Arnold diffusion problem', asserting that a generic, integrable Hamiltonian system subjected to a small perturbation has solutions that travel 'wildly and arbitrarily far' in the phase space. We will present a topological approach to the Hamiltonian instability problem. We will apply this to detect diffusing orbits under rather explicit conditions on the unperturbed system and on the perturbation. The topological method is constructive and can be implemented in numerical experiments. We will show some applications to space mission design.

The City College of New YorkCUNY
Instagram iconFacebook iconLinkedIn iconYouTube icon
© The City College of New York. All rights reserved.