Ulam method for the Chirikov standard map

  title={Ulam method for the Chirikov standard map},
  author={Klaus M. Frahm and Dima L. Shepelyansky},
  journal={The European Physical Journal B},
AbstractWe introduce a generalized Ulam method and apply it to symplectic dynamical maps with a divided phase space. Our extensive numerical studies based on the Arnoldi method show that the Ulam approximant of the Perron-Frobenius operator on a chaotic component converges to a continuous limit. Typically, in this regime the spectrum of relaxation modes is characterized by a power law decay for small relaxation rates. Our numerical data show that the exponent of this decay is approximately… 
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