# One-parameter families of brake orbits in dynamical systems

Colloquium Mathematicae (1999)

- Volume: 82, Issue: 2, page 201-217
- ISSN: 0010-1354

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topBakker, Lennard. "One-parameter families of brake orbits in dynamical systems." Colloquium Mathematicae 82.2 (1999): 201-217. <http://eudml.org/doc/210757>.

@article{Bakker1999,

abstract = {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.},

author = {Bakker, Lennard},

journal = {Colloquium Mathematicae},

keywords = {nonequilibrium solution; brake orbit; periodic brake orbits},

language = {eng},

number = {2},

pages = {201-217},

title = {One-parameter families of brake orbits in dynamical systems},

url = {http://eudml.org/doc/210757},

volume = {82},

year = {1999},

}

TY - JOUR

AU - Bakker, Lennard

TI - One-parameter families of brake orbits in dynamical systems

JO - Colloquium Mathematicae

PY - 1999

VL - 82

IS - 2

SP - 201

EP - 217

AB - 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.

LA - eng

KW - nonequilibrium solution; brake orbit; periodic brake orbits

UR - http://eudml.org/doc/210757

ER -

## References

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