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Rigorous diffusion properties for the sawtooth map

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Abstract

We get a rigorous bound for the diffusion constant of the hamiltonian dynamical system generated by a sawtooth map on a cylinder. The momentum variable properly renormalized then behaves almost like a brownian motion in the limit of infinite coupling constants. The strategy of the proof is a rigorous reformulation of the Random Phase Approximation.

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Author notes

  1. J. Bellissard

    Present address: Wissenschaftskolleg zu Berlin, Germany

Authors and Affiliations

  1. Centre de Physique Theorique, C.N.R.S. Luminy, Case 907, F-13288, Marseille Cedex 9, France

    J. Bellissard

  2. Université de Provence, Marseille

    S. Vaienti

Authors
  1. J. Bellissard
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  2. S. Vaienti
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Additional information

Communicated by T. Spencer

Supported by Contract CEE n0 SC1*0281

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Bellissard, J., Vaienti, S. Rigorous diffusion properties for the sawtooth map. Commun.Math. Phys. 144, 521–536 (1992). https://doi.org/10.1007/BF02099181

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  • DOI: https://doi.org/10.1007/BF02099181

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