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Ergodic Properties of Invariant Measures for Piecewise Monotonic Transformations

  • Chapter
The Theory of Chaotic Attractors

Abstract

During the last decade a lot of research has been done on onedimensional dynamics. Different kinds of invariant measures for certain classes of piecewise monotonic transformations have been considered. In most of these cases the Perron-Frobenius-operator plays an important role. In this paper we try to unify these different examples, which are discussed in detail below. First we give a discription of the results proved in this paper.

Research for this paper was done, when the first author visited the Institut für mathematische Statistik, Göttingen

The second author was supported by the Deutsche Forschungsgemeinschaft

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090, Wien, Austria

    Franz Hofbauer

  2. Institut für Mathematische Statistik der Universität, Lotzestraße 13, D-3400, Göttingen, Federal Republic of Germany

    Gerhard Keller

Authors
  1. Franz Hofbauer
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  2. Gerhard Keller
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Editor information

Editors and Affiliations

  1. Institute for Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA

    Brian R. Hunt

  2. Department of Mathematics, Michigan State University, 48824, East Lansing, Michigan, USA

    Tien-Yien Li

  3. Department of Mathematics, University of Delaware, 19716, Newark, Delaware, USA

    Judy A. Kennedy

  4. Department of Econometrics, University of Groningen, NL-9700 AV, Groningen, The Netherlands

    Helena E. Nusse

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© 1982 Springer Science+Business Media New York

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Hofbauer, F., Keller, G. (1982). Ergodic Properties of Invariant Measures for Piecewise Monotonic Transformations. In: Hunt, B.R., Li, TY., Kennedy, J.A., Nusse, H.E. (eds) The Theory of Chaotic Attractors. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21830-4_10

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  • DOI: https://doi.org/10.1007/978-0-387-21830-4_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-2330-1

  • Online ISBN: 978-0-387-21830-4

  • eBook Packages: Springer Book Archive

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