Periodic orbits of the sawtooth maps

DOI10.1016/0167-2789(88)90104-2zbMath0648.58027OpenAlexW2050909018MaRDI QIDQ1105251

Franco Vivaldi, Nigel Bird

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0167-2789(88)90104-2

zbMATH Keywords

chaosperiodic orbitsAnosov systemssawtooth mapsarithmetic and symbolic dynamicschaotic area-preserving mapsperturbed Anosov orbits

Mathematics Subject Classification ID

Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items

A chaotic lattice field theory in one dimension* ⋮ On the quantum cat and sawtooth maps -- return to generic behaviour ⋮ Hamiltonian transport on unstable periodic orbits ⋮ Extended symbolic dynamics in bistable CML: Existence and stability of fronts ⋮ Semiclassical theory of the sawtooth map ⋮ Recycling diffusion in sawtooth and cat maps ⋮ Rigorous diffusion properties for the sawtooth map ⋮ Ergodic properties of the discontinuous sawtooth map ⋮ On the global orbits in a bistable CML ⋮ Dynamics of some piecewise smooth Fermi-Ulam models ⋮ Resonances and transport in the sawtooth map ⋮ Statistical properties of actions of periodic orbits ⋮ Arithmetic exponents in piecewise-affine planar maps

Cites Work

• Transport in Hamiltonian systems
• A linear code for the sawtooth and cat maps
• Arithmetical properties of strongly chaotic motions
• Newton method for highly unstable orbits
• Regular and stochastic motion
• A variational principle for invariant tori of fixed frequency
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