5 papers
Rigorous verification of period-doubling bifurcations in maps
Olivier Hénot, Jean-Philippe Lessard
We present a computer-assisted approach for proving period-doubling bifurcations in one-parameter families of maps on . We solve a square augmented…
Efficient Rigorous Continuation via Chebyshev Series Expansion I
Maxime Breden, Olivier Hénot
We study the global continuation of solution manifolds arising in dynamical systems. We present a rigorous continuation method based on a Chebyshev series expansion of the solution…
Computer-Assisted Proofs in Dynamical Systems: A Case Study of a Heteroclinic Orbit in the Shimizu--Morioka System
Olivier Hénot, Akitoshi Takayasu
The radii polynomial approach is an a posteriori validation method based on the contraction of a quasi-Newton operator. We apply this strategy to give a computer-assisted proof of…
Numerical computation of transverse homoclinic orbits for periodic solutions of delay differential equations
Olivier Hénot, Jean-Philippe Lessard, Jason D. Mireles James
We present a computational method for studying transverse homoclinic orbits for periodic solutions of delay differential equations, a phenomenon that we refer to as the \emph{Poinc…
Constructive proofs for localized radial solutions of semilinear elliptic systems on
Jan Bouwe van den Berg, Olivier Hénot, Jean-Philippe Lessard
Ground state solutions of elliptic problems have been analyzed extensively in the theory of partial differential equations, as they represent fundamental spatial patterns in many m…