Highly accurate discretisation of transfer operators in Anosov dynamics (CONTRIBUTED TALK)
speaker: Caroline Wormell (Australian National University)abstract: Many key ergodic properties of chaotic systems, such as resonances, invariant measures and Lyapunov exponents, are encoded in the eigendata of transfer operators. These cannot in general be expressed analytically, and their computational study is therefore a key element of the mathematician's toolbox. However, Anosov systems, which include geodesic flows, have eigenfunctions that are hyper-distributions (functions with a negative level of differentiability). This makes the ergodic properties of most Anosov systems very difficult to numerically access. In this talk, I will present a modified Chebyshev-Lagrange interpolation algorithm that can approximate these objects very effectively in all phase space geometries. The error of the estimates can be proven to decay exponentially with the resolution of the approximation. I will give examples of how these algorithms can be used to obtain new mathematical insight, and explain how the ideas of the proof help to make sense of the output of data-driven Dynamic Mode Decomposition algorithms used in the physical sciences.
timetable:
Mon 20 May, 15:00 - 15:30, Aula Dini
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