Flux, resonances and the devil's staircase for the sawtooth map
- 1 May 1989
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 2 (2) , 347-356
- https://doi.org/10.1088/0951-7715/2/2/009
Abstract
The sawtooth mapping is a family of uniformly hyperbolic, piecewise linear, area-preserving maps on the cylinder. The authors construct the resonances, cantori and turnstiles of this family and derive exact formulae for the resonance areas and the escaping fluxes. The resonances are shown to fill the full measure of phase space. These results are extended to piecewise linear, continuous mapping for parameters which have no invariant tori. Resonance area and fluxes are of prime interest for an understanding of the deterministic transport which occurs in the stochastic regime.Keywords
This publication has 14 references indexed in Scilit:
- Resonances and Diffusion in Periodic Hamiltonian MapsPhysical Review Letters, 1989
- Periodic orbits of the sawtooth mapsPhysica D: Nonlinear Phenomena, 1988
- Area as a devil's staircase in twist mapsPhysics Letters A, 1987
- A linear code for the sawtooth and cat mapsPhysica D: Nonlinear Phenomena, 1987
- Resonances in area-preserving mapsPhysica D: Nonlinear Phenomena, 1987
- Transport in Hamiltonian systemsPhysica D: Nonlinear Phenomena, 1984
- Exact models with a complete Devil's staircaseJournal of Physics C: Solid State Physics, 1983
- The twist map, the extended Frenkel-Kontorova model and the devil's staircasePhysica D: Nonlinear Phenomena, 1983
- Critical behavior of a KAM surface: I. Empirical resultsJournal of Statistical Physics, 1982
- Rigorously diffusive deterministic mapPhysical Review A, 1981