Topological dynamics: rigorous numerics via cubical homology (Q2912385)
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scientific article; zbMATH DE number 6082691
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Topological dynamics: rigorous numerics via cubical homology |
scientific article; zbMATH DE number 6082691 |
Statements
14 September 2012
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computer assisted proof
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rigorous numerics
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interval arithmetic
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chaotic dynamics
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Conley index
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index pair
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cubical set
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homology algorithm
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reduction methods
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Topological dynamics: rigorous numerics via cubical homology (English)
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The paper presents an overview of a method of computer assisted proofs in dynamics, developed mainly by the author and his collaborators. The method is based on the Conley index theory and makes use of computations of homology of some cubical sets and maps, frequently obtained by a numerical approximation of systems of ordinary differential equations. Examples of applications include proofs of the existence of complicated dynamics in the Lorenz equations and the Hénon map, time series analysis of experiments, and databases for multiparameter systems.NEWLINENEWLINEFor the entire collection see [Zbl 1245.55001].
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