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math.DS2025
Rigorous enclosure of Lyapunov exponents of stochastic flows
Maxime Breden, Hugo Chu, Jeroen S. W. Lamb +1
We develop a powerful and general method to provide rigorous and accurate upper and lower bounds for Lyapunov exponents of stochastic flows. Our approach is based on computer-assis…
math.DS2025
Detecting random bifurcations via rigorous enclosures of large deviations rate functions
Alexandra Blessing, Alex Blumenthal, Maxime Breden +1
The main goal of this work is to provide a description of transitions from uniform to non-uniform snychronization in diffusions based on large deviation estimates for finite time L…
math.DS2024
Validated enclosure of renormalization fixed points via Chebyshev series and the DFT
Maxime Breden, Jorge Gonzalez, J. D Mireles James
This work develops a computational framework for proving existence, uniqueness, isolation, and stability results for real analytic fixed points of -th order Feigenbaum-Cvitanovi…