# Invariant jets of a smooth dynamical system

Bulletin de la Société Mathématique de France (2001)

- Volume: 129, Issue: 3, page 379-448
- ISSN: 0037-9484

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topLemaire, Sophie. "Invariant jets of a smooth dynamical system." Bulletin de la Société Mathématique de France 129.3 (2001): 379-448. <http://eudml.org/doc/272345>.

@article{Lemaire2001,

abstract = {The local deformations of a submanifold under the effect of a smooth dynamical system are studied with the help of Oseledets’ multiplicative ergodic theorem. Equivalence classes of submanifolds, called jets, are introduced in order to describe these local deformations. They identify submanifolds having the same approximations up to some order at a given point. For every order $k$, a condition on the Lyapunov exponents of the dynamical system is established insuring the convergence of the $k$-jet of a submanifold evolving under the action of the dynamical system. This condition can be satisfied even by stable dynamical systems. The limit is a $k$-jet which is invariant by the dynamical system.},

author = {Lemaire, Sophie},

journal = {Bulletin de la Société Mathématique de France},

keywords = {random dynamical systems; Lyapunov exponents; multiplicative ergodic theory; jets; Pesin theory},

language = {eng},

number = {3},

pages = {379-448},

publisher = {Société mathématique de France},

title = {Invariant jets of a smooth dynamical system},

url = {http://eudml.org/doc/272345},

volume = {129},

year = {2001},

}

TY - JOUR

AU - Lemaire, Sophie

TI - Invariant jets of a smooth dynamical system

JO - Bulletin de la Société Mathématique de France

PY - 2001

PB - Société mathématique de France

VL - 129

IS - 3

SP - 379

EP - 448

AB - The local deformations of a submanifold under the effect of a smooth dynamical system are studied with the help of Oseledets’ multiplicative ergodic theorem. Equivalence classes of submanifolds, called jets, are introduced in order to describe these local deformations. They identify submanifolds having the same approximations up to some order at a given point. For every order $k$, a condition on the Lyapunov exponents of the dynamical system is established insuring the convergence of the $k$-jet of a submanifold evolving under the action of the dynamical system. This condition can be satisfied even by stable dynamical systems. The limit is a $k$-jet which is invariant by the dynamical system.

LA - eng

KW - random dynamical systems; Lyapunov exponents; multiplicative ergodic theory; jets; Pesin theory

UR - http://eudml.org/doc/272345

ER -

## References

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- [11] V. Oseledets – « A multiplicative ergodic theorem. Lyapunov characteristic number for dynamical systems », Trans. Moscow Math. Soc.19 (1968), p. 197–231. Zbl0236.93034
- [12] Y. Pesin – « Families of invariant manifolds corresponding to nonzero characteristic exponents », Math. USSR Izvestija10 (1976), p. 1261–1305. Zbl0383.58012
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