# Ulam method for the Chirikov standard map

@article{Frahm2010UlamMF,
title={Ulam method for the Chirikov standard map},
author={Klaus M. Frahm and Dima L. Shepelyansky},
journal={The European Physical Journal B},
year={2010},
volume={76},
pages={57-68}
}
• Published 8 April 2010
• Physics
• 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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