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We 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 ...
Ulam method and fractal Weyl law for Perron--Frobenius operators
Ulam method fractal Weyl law Perron--Frobenius operators
2010/4/7
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 that the spectrum is characterized by the ...