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arXiv · 1304.2662

Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems

Martin J. Körber·Matthias Michler·Arnd Bäcker·Roland Ketzmerick
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Abstract

In open chaotic systems the number of long-lived resonance states obeys a fractal Weyl law, which depends on the fractal dimension of the chaotic saddle. We study the generic case of a mixed phase space with regular and chaotic dynamics. We find a hierarchy of fractal Weyl laws, one for each region of the hierarchical decomposition of the chaotic phase-space component. This is based on our observation of hierarchical resonance states localizing on these regions. Numerically this is verified for the standard map and a hierarchical model system.

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Martin J. Körber, Matthias Michler, Arnd Bäcker, Roland Ketzmerick. 2013-04-09. Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems. https://doi.org/10.1103/physrevlett.111.114102

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