# Ulam method and fractal Weyl law for Perron-Frobenius operators

@article{Ermann2010UlamMA,
title={Ulam method and fractal Weyl law for Perron-Frobenius operators},
author={Leonardo Ermann and Dima L. Shepelyansky},
journal={The European Physical Journal B},
year={2010},
volume={75},
pages={299-304}
}
• Published 27 December 2009
• Physics, Mathematics
• The European Physical Journal B
We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we…
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