Invariant Curves and Explosion of Periodic Islands in Systems of Piecewise Rotations

DOI10.1137/040605394zbMath1090.37029OpenAlexW1971966413WikidataQ61951256 ScholiaQ61951256MaRDI QIDQ5700601

Arek Goetz, Peter Ashwin

Publication date: 28 October 2005

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10871/14550

zbMATH Keywords

global attractorsplanar piecewise isometrynon\-smooth invariant curvesnonuniquely ergodic interval exchange

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Dynamical systems involving maps of the interval (37E05) Combinatorial dynamics (types of periodic orbits) (37E15)

Related Items (13)

Synchronization properties of random piecewise isometries ⋮ Error diffusion on acute simplices: invariant tiles ⋮ Embeddings of interval exchange transformations into planar piecewise isometries ⋮ Mixing with piecewise isometries on a hemispherical shell ⋮ Polygonal invariant curves for a planar piecewise isometry ⋮ Invariant measures for planar piecewise isometries ⋮ Error diffusion on simplices: the structure of bounded invariant tiles ⋮ Dynamical behaviors and codings of invertible planar piecewise isometric systems ⋮ Cone exchange transformations and boundedness of orbits ⋮ On global attractors for a class of nonhyperbolic piecewise affine maps ⋮ Piecewise contractions are asymptotically periodic ⋮ Unnamed Item ⋮ Singularities of two-dimensional invertible piecewise isometric dynamics

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