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 : Dynamical systems
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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⟩

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