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Spectral Properties of Pullback Operators on Vector Bundles of a Dynamical System by Allan M. Avila; Igor Mezić is a Physics and Astronomy article available to read on EtoBox.
What is Spectral Properties of Pullback Operators on Vector Bundles of a Dynamical System about?
The spectrum of the Koopman operator has been shown to encode many important statistical and geometric properties of a dynamical system. In this work, we consider induced linear operators acting on the space of sections of the state space's tangent, cotangent, and tensor bundles. We first demonstrate how these operators are natural generalizations of Koopman operators acting on functions. We then draw connections between the various operators' spectra and characterize the algebraic and differential topological properties of their spectra. We describe the discrete spectrum of these operators for linear dynamical systems and derive spectral expansions for linear vector fields. We define the notion of an ``eigendistribution,"" provide conditions for an eigendistribution to be integrable, and demonstrate how to recover the foliations arising from their integral manifolds. Last, we demonstrate that the characteristic Lyapunov exponents of a uniformly hyperbolic dynamical system are in the spectrum of the induced operators on sections of the tangent or cotangent bundle. We conclude with an application to differential geometry where the well-known fact that the flows of commuting vector f
Who reads Spectral Properties of Pullback Operators on Vector Bundles of a Dynamical System?
It is typically read by researchers, students, and practitioners in Physics and Astronomy.
- Author
- Allan M. Avila; Igor Mezić
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Published
- 2023
- Language
- EN
- Field
- Physics and Astronomy (Physical Sciences)