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Topological techniques for efficient rigorous computation in dynamics
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DOI：10.1017/s0962492902000065.png)
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We describe topological methods for the efficient, rigorous computation of
dynamical systems. In particular, we indicate how Conley's Fundamental
Decomposition Theorem is naturally related to combinatorial approximations
of dynamical systems. Furthermore, we show that computations of Morse
decompositions and isolating blocks can be performed efficiently. We conclude
with examples indicating how these ideas can be applied to finite- and infinite-dimensional
discrete and continuous dynamical systems.
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