Topological methods and Hamiltonian instability

Marian Gidea (Yeshiva University)

09-Dec-2020, 20:00-21:00 (3 years ago)

Abstract: Instability of Hamiltonian systems is relevant to problems from celestial mechanics, particle accelerators, plasma confinement, quasigeostrophic flows, etc. Motivated by such applications, one is interested in detecting mechanisms of instability in concrete models, and in providing quantitative information on the unstable trajectories.

We will describe a topological method based on `correctly aligned windows', which can be used to derive properties concerning the long-term behavior of dynamical systems. In particular, this method enables one to detect topological horseshoes. The method can be implemented in computer assisted proofs, via validated numerical computations. We will show application of this method to Hamiltonian instability. Concrete examples will include mechanical systems consisting of rotators and penduli, and the three-body problem in celestial mechanics.

analysis of PDEsclassical analysis and ODEsfluid dynamics

Audience: researchers in the topic


Online Northeast PDE and Analysis Seminar

Organizers: Javier Gomez-Serrano, Benoit Pausader*, Fabio Pusateri, Ian Tice*
*contact for this listing

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