Invariant jets of a smooth dynamical system (Q2773557)
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scientific article; zbMATH DE number 1710194
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Invariant jets of a smooth dynamical system |
scientific article; zbMATH DE number 1710194 |
Statements
Invariant jets of a smooth dynamical system (English)
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24 February 2002
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random dynamical systems
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Lyapunov exponents
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Oseledets' multiplicative ergodic theory
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jets
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Pesin theory
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This paper deals with the local deformations of a submanifold under the effect of smooth dynamical system. To this end the author uses of Oseledets' multiplicative ergodic theorem and introduces equivalence classes of submanifolds, called jets. They (equivalence classes) identify submanifolds having the same approximations up to some order at a given point. The author presents a condition for the Lyapunov exponent of the dynamical system guaranteeing the convergence of the \(k\)-jet of a submanifold evolving under the action. The author shows that this condition holds even for stable dynamical system and the limit is a \(k\)-jet which is invariant for the dynamical system.
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0.7148442268371582
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