Computer Science – Numerical Analysis
Scientific paper
Jan 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cemec..38...23h&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 38, Jan. 1986, p. 23-66. In French.
Computer Science
Numerical Analysis
4
Analytic Geometry, Degrees Of Freedom, Dynamical Systems, Numerical Analysis, Particle Motion, Ergodic Process, Orbits, Periodic Variations, Surface Stability, Symmetry, Topology
Scientific paper
The properties of a two-degree-of-freedom dynamical system defined by particle motion in a C1 generalized billiard are numerically analyzed. The periodic orbit along a billiard's small diameter is stable or unstable (in the linear approximation) according to the position of each relevant arc center with respect to the opposite one. When an arc center lies on the opposite arc, two different transition patterns ranging from order to chaos are observed for the same billiard. The total area of nonchaotic regions is greater for symmetric billiards. Peanut-shaped billiards always appear to be ergodic, and transverse invariant curves appear to be common for billiards with two axes of symmetry. It is concluded that C1 generalized billiards are inadequate models for smooth mappings.
Dumont Th.
Hayli Avram
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