Authors: Jason D. Mireles James and Rafael de la Llave.
Abstract: We develop and implement computer assisted arguments which establish the existence of heteroclinic/homoclinic connecting orbits between fixed points of compact infinite dimensional maps. The argument is based on a-posteriori analysis of a certain "finite time boundary value problem". A key ingredient in the analysis is the representation of local stable/unstable manifolds of the fixed point. For a compact mapping the stable manifold is infinite dimensional and an important component of the present work is the development of computer assisted error bounds for numerical approximations of this manifold. As an illustration of the utility of these methods we prove the existence of some connecting orbits for a nonlinear dynamical system studied in the mathematical ecology literature.
SIADS, Vol. 15, No. 2, pp. 1268-1323 (2016).
Computer Assisted Proof Codes: (codes require the IntLab package)