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Asymptotic Periodicity of Markov and Related Operators

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Dynamics Reported

Part of the book series: Dynamics Reported ((DYNAMICS,volume 2))

Abstract

The aim of this paper is to provide a unified exposition of some results in the theory of asymptotic behaviour of Markov (and related) operators. These results followed the invited address of A. Lasota at ICM ’82. He introduced the notion of constrictive operators saying that an operator P is weakly (strongly) constrictive if there exists a weakly (strongly) compact set F such that all trajectories of densities converge in L 1 norm to F. Lasota et al. investigated the asymptotic periodicity of Markov operators and proved that it holds for

  1. (i)

    strongly constrictive Markov operators [14]

  2. (ii)

    weakly constrictive Frobenius-Perron operators [19].

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Authors
  1. J. Komorník
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Editor information

Editors and Affiliations

  1. Division of Applied Mathematics, Brown University, 02912, Providence, Rhode Island, USA

    C. K. R. T. Jones

  2. Mathematics, Swiss Frderal Institute of Technology (ETH), CH-8092, Zürich, Switzerland

    U. Kirchgraber

  3. Mathematics, Ludwig-Maximilians University, W-8000, Munich, Federal Republic of Germany

    H. O. Walther

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© 1993 Springer-Verlag Berlin Heidelberg

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Komorník, J. (1993). Asymptotic Periodicity of Markov and Related Operators. In: Jones, C.K.R.T., Kirchgraber, U., Walther, H.O. (eds) Dynamics Reported. Dynamics Reported, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61232-9_2

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  • DOI: https://doi.org/10.1007/978-3-642-61232-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64755-0

  • Online ISBN: 978-3-642-61232-9

  • eBook Packages: Springer Book Archive

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