The Clarkson Center for Complex Systems Science
Hugo Chu, PhD Student Dept of Mathematics, Imperial College London
Will present a talk entitled:
Rigorous enclosures of Lyapunov exponents of stochastic flows
Abstract: I will present a novel powerful and general method to provide arbitrarily accurate rigorous upper and lower bounds for Lyapunov exponents of stochastic flows. Our approach is based on computer-assisted tools, the adjoint method and established results on the ergodicity of diffusion processes. We do not require any structural assumptions on the stochastic system and work under mild hypoellipticity conditions outside of perturbative regimes. Therefore, our method allows for the treatment of systems that were so far inaccessible from existing mathematical tools. We demonstrate our method to exhibit the chaotic nature of three non-Hamiltonian systems. Finally, we show that our method is robust to continuation methods to give bounds on Lyapunov exponents for ranges of parameters.This is joint work with Maxime Breden (Ecole Polytechnique Paris), Jeroen Lamb (Imperial College London) and Martin Rasmussen (Imperial College London)
Bio: Hugo is a final year PhD student in Mathematics at Imperial College London. He is currently visiting the Centre de recherches mathématiques, Montreal. He is mainly interested in computer-assisted methods and Numerical Analysis to solve nonlinear problems. In particular, his research is focused on problems arising from Random Dynamical Systems and in the rigorous resolution of nonlinear partial differential equations.
SC166
November 8, 2024
12:00 pm
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C3S2 Clarkson Center for Complex Systems Science l http://webspace.clarkson.edu/~ebollt/Website-C3S2/index.html
CLARKSON UNIVERSITY l Potsdam, New York 13699-5720