Displaying similar documents to “On chaotic dynamics in rational polygonal billiards.”

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...

Eight-shaped Lissajous orbits in the Earth-Moon system

Grégory Archambeau, Philippe Augros, Emmanuel Trélat (2011)

MathematicS In Action

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Euler and Lagrange proved the existence of five equilibrium points in the circular restricted three-body problem. These equilibrium points are known as the Lagrange points (Euler points or libration points) L 1 , ... , L 5 . The existence of families of periodic and quasi-periodic orbits around these points is well known (see [, , , , ]). Among them, halo orbits are 3-dimensional periodic orbits diffeomorphic to circles. They are the first kind of the so-called Lissajous orbits. To be selfcontained,...

E -orbit functions.

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

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

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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...

Orbit functions.

Klimyk, Anatoliy, Patera, Jiri (2006)

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

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A note on dynamical zeta functions for S-unimodal maps

Gerhard Keller (2000)

Colloquium Mathematicae

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Let f be a nonrenormalizable S-unimodal map. We prove that f is a Collet-Eckmann map if its dynamical zeta function looks like that of a uniformly hyperbolic map.

Antisymmetric orbit functions.

Klimyk, Anatoliy, Patera, Jiri (2007)

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

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