Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps

@article{Arnoldi2015AsymptoticSG,
  title={Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps},
  author={Jean‐François Arnoldi and F. Faure and Tobias Weich},
  journal={Ergodic Theory and Dynamical Systems},
  year={2015},
  volume={37},
  pages={1 - 58}
}
We consider a simple model of an open partially expanding map. Its trapped set ${\mathcal{K}}$ in phase space is a fractal set. We first show that there is a well-defined discrete spectrum of Ruelle resonances which describes the asymptotic of correlation functions for large time and which is parametrized by the Fourier component $\unicode[STIX]{x1D708}$ in the neutral direction of the dynamics. We introduce a specific hypothesis on the dynamics that we call ‘minimal captivity’. This hypothesis… 
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