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.
@article{bwmeta1.element.bwnjournal-article-cmv82i2p201bwm,
author = {Lennard Bakker},
title = {One-parameter families of brake orbits in dynamical systems},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {201-217},
zbl = {0988.37077},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv82i2p201bwm}
}
Bakker, Lennard. One-parameter families of brake orbits in dynamical systems. Colloquium Mathematicae, Tome 79 (1999) pp. 201-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv82i2p201bwm/
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