Rigorous connecting orbits from numerics
- Kenneth J. Palmer (National Taiwan University, currently visiting Alpen-Adria University, Klagenfurt, Austria)
Abstract
Rigorous numerical methods for establishing the existence of connecting orbits in systems of autonomous differential equations are presented.
Previously we studied the existence of a transversal connecting orbit from one hyperbolic periodic orbit to another. Given a suitable approximate connecting orbit and assuming that a certain associated linear operator is invertible, the existence of a true connecting orbit near the approximate orbit provided the approximate orbit is sufficiently "good" was proved.
More recently we studied orbits connecting hyperbolic equilibria in a parametrized autonomous system. Given a suitable approximate connecting orbit and assuming that a certain associated matrix is invertible, the existence of a true connecting orbit near the approximate orbit and for a nearby parameter value is proved provided the approximate orbit is sufficiently "good".
