Constructive methods for the long term analysis of dynamics

Abstract: The long term behavior of dynamical systems is an important practical problem in technology and a deep challenge for mathematics. In this set of lectures, we plan to present some ideas of a concrete methodology that can be used to study the long term dynamics of some given systems. The key idea is to:

• Identify some geometric structures that imply interesting long term behaviors.
• Develop rigorous methods that, with a finite computations can establish the existence of these objects in concrete systems.

We can only cover some generalities and some vignettes that illustrate these program both in finite dimensional problems and in infinite dimensional systems. This first lecture will present some of the main tools from analysis and topology.

analysis of PDEsclassical analysis and ODEsfluid dynamics

Audience: researchers in the topic

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Online Northeast PDE and Analysis Seminar

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