Polygonal invariant curves for a planar piecewise isometry

DOI10.1090/S0002-9947-05-03670-6zbMath1080.37009WikidataQ61951254 ScholiaQ61951254MaRDI QIDQ5694988

Arek Goetz, Peter Ashwin

Publication date: 6 October 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

symbolic dynamicsinvariant curvesperiodic pointspolynomial complexityinterval exchange transformationcellsplanar piecewise isometry

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Modular representations and characters (20C20) Cyclotomic extensions (11R18) Symbolic dynamics (37B10) Combinatorial dynamics (types of periodic orbits) (37E15)

Related Items (13)

An example of PET. Computation of the Hausdorff dimension of the aperiodic set ⋮ Embeddings of interval exchange transformations into planar piecewise isometries ⋮ Dynamics of a continuous piecewise affine map of the square ⋮ Invariant measures for planar piecewise isometries ⋮ Dynamical behaviors and codings of invertible planar piecewise isometric systems ⋮ Dissipative outer billiards: a case study ⋮ Cone exchange transformations and boundedness of orbits ⋮ On global attractors for a class of nonhyperbolic piecewise affine maps ⋮ Asymptotic periodicity in outer billiards with contraction ⋮ “Metric” complexity for weakly chaotic systems ⋮ Global properties of a family of piecewise isometries ⋮ Unnamed Item ⋮ Singularities of two-dimensional invertible piecewise isometric dynamics

Cites Work

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• Dual polygonal billiards and necklace dynamics
• Dynamics of a piecewise rotation
• On the geometry of orientation-preserving planar piecewise isometries
• On the dual billiard problem
• Embedding dynamics for round-off errors near a periodic orbit
• Dynamics of non-ergodic piecewise affine maps of the torus
• Piecewise isometries have zero topological entropy
• Rank two interval exchange transformations
• Topological entropy of generalized polygon exchanges
• Tangencies in invariant disc packings for certain planar piecewise isometries are rare
• Dynamics of symplectic piecewise affine elliptic rotation maps on tori
• Rotations by  /7
• Quadratic rational rotations of the torus and dual lattice maps
• Recursive tiling and geometry of piecewise rotations by  /7
• Perturbations of 8-Attractors and Births of Satellite Systems
• Invariant Curves and Explosion of Periodic Islands in Systems of Piecewise Rotations
• Hamiltonian mappings and circle packing phase spaces

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