We develop techniques for computing the (un) stable manifold at a hyperbolic equilibrium of
an analytic vector field. Our approach is based on the so-called parametrization method for …

In this work we develop a computer-assisted technique for proving existence of periodic
solutions of nonlinear differential equations with non-polynomial nonlinearities. We exploit …

In this work we introduce a rigorous computational method for finding heteroclinic solutions
of a system of two second order differential equations. These solutions correspond to …

In this work we develop some automatic procedures for computing high order polynomial
expansions of local (un) stable manifolds for equilibria of differential equations. Our method …

Wright's conjecture states that the origin is the global attractor for the delay differential
equation y′(t)=− α y (t− 1)[1+ y (t)] for all α∈(0, π 2] when y (t)>− 1. This has been proven to …

We develop a rigorous numerical method to compare local minimizers of the Ohta–
Kawasaki functional in two dimensions. In particular, we validate the phase diagram …

We study polynomial expansions of local unstable manifolds attached to equilibrium
solutions of parabolic partial differential equations. Due to the smoothing properties of …

We present numerical results and computer assisted proofs of the existence of periodic
orbits for the Kuramoto--Sivashinky equation. These two results are based on writing down …

We use validated numerical methods to prove the existence of spatial periodic orbits in the
equilateral restricted four-body problem. We study each of the vertical Lyapunov families (up …

We develop a theoretical framework for computer-assisted proofs of the existence of
invariant objects in semilinear PDEs. The invariant objects considered in this paper are …