Global stability of a class of discontinuous dual billiards

DOI10.1007/BF01205552zbMath0653.58018WikidataQ29306557 ScholiaQ29306557MaRDI QIDQ1107889

Anna V. Shaidenko, Franco Vivaldi

Publication date: 1987

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

stabilityperiodic orbitsdiscontinuous area-preserving maps

Mathematics Subject Classification ID

Ergodic theory (37A99) Stability theory for smooth dynamical systems (37C75) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (21)

Dynamical properties of 2-torus parabolic maps ⋮ Outer billiards with contraction: regular polygons ⋮ Pseudochaotic dynamics near global periodicity ⋮ Nonlinear rotations on a lattice ⋮ Book Review: Outer billiards on kites ⋮ Survey lecture on billiards ⋮ On codings and dynamics of planar piecewise rotations ⋮ Dual polygonal billiards and necklace dynamics ⋮ A proof of Culter's theorem on the existence of periodic orbits in polygonal outer billiards ⋮ Negative refraction and tiling billiards ⋮ Piecewise isometries, uniform distribution and 3log 2−π²/8 ⋮ Dissipative outer billiards: a case study ⋮ Asymptotic periodicity in outer billiards with contraction ⋮ Tangents-free property in invariant disk packings generated by some general planar piecewise isometries ⋮ On Moser’s boundedness problem of dual Billiards ⋮ Tangencies in invariant disc packings for certain planar piecewise isometries are rare ⋮ Hamiltonian mappings and circle packing phase spaces: numerical investigations ⋮ Pointwise periodic maps with quantized first integrals ⋮ Dual billiards ⋮ Asymptotic dynamics of the dual billiard transformation. ⋮ Rational dual billiards.

Cites Work

• The Benettin-Strelcyn oval billiard revisited
• Pseudointegrable systems in classical and quantum mechanics
• A piecewise linear model for the zones of instability of an area- preserving map
• Analytically solvable dynamical systems which are not integrable
• Stable and Random Motions in Dynamical Systems
• Two-Dimensional Measure-Preserving Mappings
• Number fields
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