Model
Digital Document
Publisher
Florida Atlantic University
Description
In this dissertation we present a computational approach to Conley's Decomposition
Theorem, which gives a global decomposition of dynamical systems, and
introduce an explicit numerical algorithm with computational complexity bounds
for computing global dynamical structures of a continous map including attractorrepeller
pairs and Conley's Lyapunov function. The approach is based on finite spatial
discretizations and combinatorial multivalued maps. The method is successful
in exhibiting approximations of attractor-repeller pairs, invariant sets, and Conley's
Lyapunov function. We used the C++ language to code the algorithm.
Theorem, which gives a global decomposition of dynamical systems, and
introduce an explicit numerical algorithm with computational complexity bounds
for computing global dynamical structures of a continous map including attractorrepeller
pairs and Conley's Lyapunov function. The approach is based on finite spatial
discretizations and combinatorial multivalued maps. The method is successful
in exhibiting approximations of attractor-repeller pairs, invariant sets, and Conley's
Lyapunov function. We used the C++ language to code the algorithm.
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