Olivier Hénot
École Polytechnique, Centre de Mathématiques Appliquées
I specialize in the study of nonlinear differential equations, particularly those set on infinite dimensional spaces, such as delay and partial differential equations.
I investigate aspects of dynamical system theory, with a focus on invariant manifolds, connecting orbits, as well as bifurcation analysis.
This research employs numerical simulations to explore intricate dynamics, which are then rigorously coupled with analytic methods to prove ‘‘what is seen on the screen’’.
For the verification to succeed, we make a choice of function spaces, basis functions, so that the analytic estimates and the computational parameters operate conjointly to bound the errors sufficiently tightly.
This process draws from several fields, such as numerical analysis, functional analysis and approximation theory.
I also have a particular interest for applications, specifically in celestial mechanics.
Discover the astronomy picture of the day on NASA's website!
E-mail: olivier[dot]henot[at]polytechnique[dot]edu
Softwares
I am involved in two open-source (MIT license) projects, written in
Julia:
- RadiiPolynomial is a library for computer-assisted proofs in dynamical systems
- IntervalArithmetic is a library for rigorous numerics via interval arithmetic
Publications
- O. Hénot, J.-P. Lessard and J. D. Mireles James, Numerical computation of transverse homoclinic orbits for periodic solutions of delay differential equations, SIAM Journal on Applied Dynamical Systems, 22 (2023), 3093-3129.
- J. B. van den Berg, O. Hénot and J.-P. Lessard, Constructive proofs for localised radial solutions of semilinear elliptic systems on \(\mathbb{R}^d\), Nonlinearity, 36 (2023), 6476.
- K. E. M. Church, O. Hénot, P. Lappicy, J.-P. Lessard and H. Sprink, Periodic orbits in Hořava-Lifshitz cosmologies, General Relativity and Gravitation, 55 (2022), 2.
- O. Hénot, J.-P. Lessard and J. D. Mireles James, Parameterization of unstable manifolds for DDEs: formal series solutions and validated error bounds, Journal of Dynamics and Differential Equations, 34 (2022), 1285–1324.
- O. Hénot, On polynomial forms of nonlinear functional differential equations, Journal of Computational Dynamics, 8 (2021), 307-323.
- O. Hénot and C. Rousseau, Spiderweb central configurations, Qualitative Theory of Dynamical Systems, 18 (2019), 1135–1160.