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One-parameter families of brake orbits in dynamical systems

Lennard Bakker — 1999

Colloquium Mathematicae

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...

Rigidity of projective conjugacy for quasiperiodic flows of Koch type

Lennard F. Bakker — 2008

Colloquium Mathematicae

For quasiperiodic flows of Koch type, we exploit an algebraic rigidity of an equivalence relation on flows, called projective conjugacy, to algebraically characterize the deviations from completeness of an absolute invariant of projective conjugacy, called the multiplier group, which describes the generalized symmetries of the flow. We then describe three ways by which two quasiperiodic flows with the same Koch field are projectively conjugate when their multiplier groups are identical. The first...

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