**
Connecting orbits for compact infinite dimensional maps:**

computer assisted proofs of existence

** 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.

** Preprint:**

"Connecting orbits for compact infinite dimensional maps:
computer assisted proofs of existence"

SIADS, Vol. 15, No. 2, pp. 1268-1323 (2016).

** Computer Assisted Proof Codes:**
(codes require the IntLab package)

Compressed
Folder Containing all the MatLab/IntLab programs
used in the paper.