# Generic Properties of Dynamical Systems

Abstract : The state of a concrete system (from physics, chemistry, ecology, or other sciences) is described using (finitely many, say n) observable quantities (e.g., positions and velocities for mechanical systems, population densities for echological systems, etc.). Hence, the state of a system may be represented as a point $x$ in a geometrical space $\mathbb R^n$. In many cases, the quantities describing the state are related, so that the phase space (space of all possible states) is a submanifold $M\subset \mathbb R^n$. The time evolution of the system is represented by a curve $x_t$, $t \in\mathbb R$ drawn on the phase space $M$, or by a sequence $x_n \in M$, $n \in\mathbb Z$, if we consider discrete time.
Keywords :
Type de document :
Article dans une revue
Encyclopedia of Mathematical Physics, Academic Press, 2006, pp. 494-502. 〈10.1016/B0-12-512666-2/00164-4〉

Littérature citée [14 références]

https://hal.archives-ouvertes.fr/hal-01348445
Contributeur : Mathias Legrand <>
Soumis le : mercredi 27 juillet 2016 - 15:20:46
Dernière modification le : mardi 23 août 2016 - 11:51:54

### Fichier

B0.pdf
Fichiers produits par l'(les) auteur(s)

### Citation

Christian Bonatti. Generic Properties of Dynamical Systems. Encyclopedia of Mathematical Physics, Academic Press, 2006, pp. 494-502. 〈10.1016/B0-12-512666-2/00164-4〉. 〈hal-01348445〉

### Métriques

Consultations de la notice

## 120

Téléchargements de fichiers