Dynamics of a family of piecewise-linear area-preserving plane maps II. Invariant circles

DOI10.1080/10236190500273127zbMath1082.37045arXivmath/0303007OpenAlexW2009246623MaRDI QIDQ3369565

Jeffrey C. Lagarias, Eric M. Rains

Publication date: 2 February 2006

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0303007

zbMATH Keywords

symbolic dynamicsNumerical experimentscircle mapsarea-preserving mapiterated mapirrational rotation numberpiecewise-linear homeomorphismsdynamics on rays

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Symbolic dynamics (37B10) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Rotation numbers and vectors (37E45)

Related Items (max. 100)

Center Bifurcation in the Lozi Map ⋮ On the Existence of Chaos in a Discontinuous Area-Preserving Map Arising in Financial Markets ⋮ Dynamics of a continuous piecewise affine map of the square ⋮ Asymptotic Poincaré maps along the edges of polytopes ⋮ Dynamics of a family of piecewise-linear area-preserving plane maps III. Cantor set spectra ⋮ Border-Collision Bifurcations in $\mathbb{R}^N$ ⋮ Critical curves of a piecewise linear map ⋮ Arithmetic exponents in piecewise-affine planar maps

Cites Work

• Unnamed Item
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Dynamics of a family of piecewise-linear area-preserving plane maps III. Cantor set spectra
• Periodic orbits of difference equations
• Dynamics of a family of piecewise-linear area-preserving plane maps I. Rational rotation numbers

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