A linear code for the sawtooth and cat maps

DOI10.1016/0167-2789(87)90037-6zbMath0647.58031OpenAlexW2064210050MaRDI QIDQ1104617

Franco Vivaldi, Ian C. Percival

Publication date: 1987

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(87)90037-6

zbMATH Keywords

periodic orbitsMorita equivalencecantoriregular singularitiesGreen function methodsholonomic \({\mathcal D}\)- moduleslinear area preserving mapssawtooth maps

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (18)

Taylor-Chirikov map package: A package of programs for the calculation of ordered periodic orbits of area preserving twist maps ⋮ A chaotic lattice field theory in one dimension* ⋮ Periodic orbits of the sawtooth maps ⋮ On the quantum cat and sawtooth maps -- return to generic behaviour ⋮ Hamiltonian transport on unstable periodic orbits ⋮ Coding chaotic billiards. I: Non-compact billiards on a negative curvature manifold ⋮ Semiclassical theory of the sawtooth map ⋮ Recycling diffusion in sawtooth and cat maps ⋮ Elliptic behaviour in the sawtooth standard map. ⋮ Rigorous diffusion properties for the sawtooth map ⋮ Ergodic properties of the discontinuous sawtooth map ⋮ Dynamics of some piecewise smooth Fermi-Ulam models ⋮ Symplectic maps, variational principles, and transport ⋮ Resonances and transport in the sawtooth map ⋮ Linear encoding of the spatiotemporal cat ⋮ Chaotic quantum motion in a space-time periodic potential: An exactly solvable model ⋮ Continuous limit of discrete sawtooth maps and its algebraic framework ⋮ Quantum to classical correspondence for the Fermi-acceleration model

Cites Work

• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• A renormalization approach to invariant circles in area-preserving maps
• Transport in Hamiltonian systems
• Solitons and condensed matter physics. Proceedings of the symposium on nonlinear (soliton) structure and dynamics in condensed matter. Oxford, England, June 27-29, 1978
• Arithmetical properties of strongly chaotic motions
• Invariant circles for the piecewise linear standard map
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Regular and stochastic motion
• Stable and Random Motions in Dynamical Systems
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