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On the rate of convergence to equilibrium in one-dimensional systems

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Abstract

We determine the essential spectral radius of the Perron-Frobenius-operator for piecewise expanding transformations considered as an operator on the space of functions of bounded variation and relate the speed of convergence to equilibrium in such one-dimensional systems to the greatest eigenvalues of generalized Perron-Frobenius-operators of the transformations (operators which yield singular invariant measures).

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Im Neuenheimer Feld 294, D-6900, Heidelberg, Germany

    Gerhard Keller

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  1. Gerhard Keller
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Communicated by O. E. Lanford

This work has been supported by the Deutsche Forschungsgemeinschaft

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Keller, G. On the rate of convergence to equilibrium in one-dimensional systems. Commun.Math. Phys. 96, 181–193 (1984). https://doi.org/10.1007/BF01240219

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  • DOI: https://doi.org/10.1007/BF01240219

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