Geodesic
One-parameter families of brake orbits in dynamical systems
Colloquium Mathematicum, Tome 82 (1999) no. 2, pp. 201-217.

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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 brake orbits is defined as well as two notions of nondegeneracy by which a given brake orbit embeds into a one-parameter family of brake orbits. The duality between the two notions of nondegeneracy for a brake orbit in a one-parameter family is described. Finally, four ways in which a given periodic brake orbit generates a one-parameter family of periodic brake orbits are detailed.
DOI : 10.4064/cm-82-2-201-217

Lennard Bakker 1

1 
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Lennard Bakker. One-parameter families of brake orbits in dynamical systems. Colloquium Mathematicum, Tome 82 (1999) no. 2, pp. 201-217. doi : 10.4064/cm-82-2-201-217. http://geodesic.mathdoc.fr/articles/10.4064/cm-82-2-201-217/

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