UnstableManifoldCompactMap
swMATH ID: 
22780

Software Authors: 
MirelesJames, J.D.

Description: 
FourierTaylor Approximation of Unstable Manifolds for Compact Maps: Numerical Implementation and Computer Assisted Error Bounds. We develop and implement a seminumerical method for computing high order Tay lor approximations of the unstable manifold at a hyperbolic fixed point of a compact infinite dimensional analytic map. Even though the method involves several layers of truncation our goal is to obtain a representation of the invariant manifold which is accurate in a large region about the fixed point. In order to insure the accuracy of our computations we develop aposteriori error bounds for the approximations. Numerical implementation of the aposteriori theory, combined with deliberate control of float ing point roundoff errors (or interval arithmetic), leads to mathematically rigorous computer assisted theorems describing precisely the truncation errors for the approxi mation of the invariant manifold. The method is illstrated for the KotSchaffer model of population dynamics. 
Homepage: 
http://cosweb1.fau.edu/~jmirelesjames/unstableManifoldCompactMapPage.html

Dependencies: 
Matlab 
Related Software: 
INTLAB;
Matlab

Cited in: 
1 Publication
