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Ergodic Theory, Boole Type Transformations, Dynamical Systems Theory

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Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

Abstract

The arithmetic properties of generalized one-dimensional ergodic Boole type transformations are studied in the framework of the operator-theoretic approach. Some invariant measure statements and ergodicity conjectures concerning generalized multi-dimensional Boole-type transformations are formulated.

Supported by 110T558-project of TUBITAK.

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Acknowledgements

The author is cordially appreciated to professor D. Blackmore (NJ, USA) for valuable discussions of the ergodic measure properties related with generalized Boole transformations.

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Authors and Affiliations

  1. Department of Applied Mathematics, AGH University of Science and Technology, Kraków, 30-059, Poland

    Anatolij K. Prykarpatski

Authors
  1. Anatolij K. Prykarpatski
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Correspondence to Anatolij K. Prykarpatski .

Editor information

Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Prykarpatski, A.K. (2015). Ergodic Theory, Boole Type Transformations, Dynamical Systems Theory. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_38

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