Chaos in iterated applications
Catastrophes and chaos in dynamic systems

Article REF: AF1405 V1

Chaos in iterated applications
Catastrophes and chaos in dynamic systems

Author : Claudine DANG VU-DELCARTE

Publication date: October 10, 2010 | Lire en français

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3. Chaos in iterated applications

Definition 15 Let be a continuous application (or transformation) :

x \to f (x), \forall x \in ℝ^{n}

^( 63 )

its inverse f ^-1 being continuous (diffeomorphism). f ^k denotes the k-th iterate of f, i.e.: f ⁰ (x) = x, f ^k (x) = f (f ^k^-1 (x)). The application f is called...

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References

(1) - ARNOLD (V.), AVEZ (A.) - Problèmes ergodiques de la mécanique classique - Gauthier-Villars (1967).
(2) - BERGE (P.), POMEAU (Y.), VIDAL (C.) - L'ordre dans le chaos - Hermann (1988).

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