Displaying similar documents to “Eight-shaped Lissajous orbits in the Earth-Moon system”

One-parameter families of brake orbits in dynamical systems

Lennard Bakker (1999)

Colloquium Mathematicae

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We give a clear and systematic exposition of one-parameter families of brake orbits in dynamical systems on product vector bundles (where the fiber has the same dimension as the base manifold). A generalized definition of a brake orbit is given, and the relationship between brake orbits and periodic orbits is discussed. The brake equation, which implicitly encodes information about the brake orbits of a dynamical system, is defined. Using the brake equation, a one-parameter family of...

E -orbit functions.

Klimyk, Anatoliy U., Patera, Jiri (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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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...

Stability and gradient dynamical systems.

Jack K. Hale (2004)

Revista Matemática Complutense

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The objective in these notes is to present an approach to dynamical systems in infinite dimensions. It does not seem reasonable to make a comparison of all of the orbits of the dynamics of two systems on non locally compact infinite dimensional spaces. Therefore, we choose to compare them on the set of globally defined bounded solutions. Fundamental problems are posed and several important results are stated when this set is compact. We then give results on the dynamical system which...