Displaying similar documents to “The accuracy of numerically computed orbits of dynamical systems”

On the existence of chaotic behaviour of diffeomorphisms

Michal Fečkan (1993)

Applications of Mathematics

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For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt.

Periodic orbits and chain-transitive sets of C1-diffeomorphisms

Sylvain Crovisier (2006)

Publications Mathématiques de l'IHÉS

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We prove that the chain-transitive sets of C-generic diffeomorphisms are approximated in the Hausdorff topology by periodic orbits. This implies that the homoclinic classes are dense among the chain-recurrence classes. This result is a consequence of a global connecting lemma, which allows to build by a C-perturbation an orbit connecting several prescribed points. One deduces a weak shadowing property satisfied by C-generic diffeomorphisms: any pseudo-orbit is approximated in the Hausdorff...

On a shadowing lemma in metric spaces

Tibor Žáčik (1992)

Mathematica Bohemica

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In the present paper conditions are studied, under which a pseudo-orbit of a continuous map f : M → M , where M is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map f .