4 papers
Numerical Analysis of differential equations on weighted Sobolev spaces: beyond classical orthogonal polynomials
Maxime Breden, Hugo Chu
We lay mathematical foundations for the Numerical Analysis of differential equations on Sobolev spaces weighted by a Gibbs probability measure $ν(\mathrm{d} x) = e^{-V(x)}\mathrm{…
Constructive proofs for some semilinear PDEs on
Maxime Breden, Hugo Chu
We develop computer-assisted tools to study semilinear equations of the form \begin{equation*} -Îu -\frac{x}{2}\cdot \nabla{u}= f(x,u,\nabla u) ,\quad x\in\mathbb{R}^d. \end{equat…
The conditioned Lyapunov spectrum for random dynamical systems
Matheus M. Castro, Dennis Chemnitz, Hugo Chu +3
We establish the existence of a full spectrum of Lyapunov exponents for memoryless random dynamical systems with absorption. To this end, we crucially embed the process conditioned…
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…