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Flux, resonances and the devil's staircase for the sawtooth map

Q Chen and J D Meiss

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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.


PACS

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

02.30.-f Function theory, analysis

MSC

37E05 Maps of the interval (piecewise continuous, continuous, smooth)

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 2 (May 1989)



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