Alex Mauroy, Nov 2013

Schedule

• 9:30 am: meet with Richard, 109 Steele
• 10:00 am: Open
• 10:30 am: Open
• 11:00 am: Prof. Oscar Bruno
• 11:30 am: Seminar prep
• 12:00 pm: Group Meeting Seminar, 213 Annenberg
• 1:15 pm: Meet with John Doyle
• 2:00 pm: Seungil You, 231 Annenberg
• 2:45 pm: Eric Wolff, 331 Annenberg
• 3:30 pm: Open
• 4:15 pm: Open

Talk Abstract

A spectral operator-theoretic approach to dissipative systems: geometry and global stability

Operator-theoretic methods provide a powerful global description of dynamical systems. They transform a nonlinear system into a linear (but infinite-dimensional) system and are therefore well-suited to spectral analysis. These methods have been largely developed over the past decades for conservative systems (i.e., on an attractor), in the context of unitary operators, but they have almost never been applied to dissipative systems (i.e., off the attractor). > In this talk, we present an operator-theoretic framework for the study of dissipative systems, which relies on the so-called Koopman operator. In particular, we show that the global geometric properties of the systems are captured by the spectral properties of the Koopman operator. For instance the well-known isochrons of limit cycles are related to an eigenfunction of the operator, an observation which yields a new method for computing them and which is used to extend the concept to other types of attractors. In addition, (global) stability properties of the system are revealed by the existence of particular eigenfunctions. This provides a new framework for the global stability analysis of general attractors.