Measurable dynamics has traditionally referred to ergodic theory, which is in some sense a
sister topic to dynamical systems and chaos theory. However, the topic has until recently …

Judicious use of interval arithmetic, combined with careful pen and paper estimates, leads to
effective strategies for computer assisted analysis of nonlinear operator equations. The …

In this paper we propose a rigorous numerical technique for the computation of symmetric
connecting orbits for ordinary differential equations. The idea is to solve a projected …

A computational method based on Chebyshev series to rigorously compute solutions of
initial and boundary value problems of analytic nonlinear vector fields is proposed. The idea …

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 paper we introduce a computational method for proving the existence of generic
saddle-to-saddle connections between equilibria of first order vector fields. The first step …

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 …

In this paper, we use rigorous numerics to compute several global smooth branches of
steady states for a system of three reaction-diffusion PDEs introduced by Iida et al.[J. Math …