Quasiregularity and rigorous diffusion of strong Hamiltonian chaos.
Exact results are derived concerning quasiregularity and diffusion of strong chaos on resonances of the sawtooth map. A chaotic ensemble of well-defined quasiregularity type (the sequence of resonances visited) is generally a fractal set whose main characteristics, the topological entropy and the Hausdorff dimension, are calculated exactly, under some conditions, using a symbolic dynamics. The effect of quasiregularity on chaotic diffusion is characterized by an infinity of diffusion coefficients, each associated with a fractal ensemble trapped in a periodic set of resonances. In some cases, these coefficients are calculated exactly and it is shown that rigorous diffusion takes place on the resonances.
Barash
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Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Dana
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