3 papers
math.AP2026
Constructive existence proofs and stability of stationary solutions to parabolic PDEs using Gegenbauer polynomials
Maxime Breden, Matthieu Cadiot, Antoine Zurek
In this paper, we present a computer-assisted framework for constructive proofs of existence for stationary solutions to one-dimensional parabolic PDEs and the rigorous determinati…
math.DS2024
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.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…