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Introduction and Examples

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Transfer Operators, Endomorphisms, and Measurable Partitions

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2217))

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Abstract

We present a unified study a class of positive operators called (generalized) transfer operators, and of their applications to the study of endomorphisms, measurable partitions, and Markov processes, as they arise in diverse settings. We begin with the setting of dynamics in standard Borel, and measure, spaces.

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Notes

  1. 1.

    We reserve the symbol σ for an endomorphism of a standard Borel space \((X, {\mathcal B})\), so that to avoid any confusion we write sigma-algebra and sigma-finite measure instead of such more common terms σ-algebra and σ-finite.

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Authors and Affiliations

  1. Department of Mathematics, University of Iowa, Iowa City, Iowa, USA

    Sergey Bezuglyi & Palle E. T. Jorgensen

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  1. Sergey Bezuglyi
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  2. Palle E. T. Jorgensen
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Bezuglyi, S., Jorgensen, P.E.T. (2018). Introduction and Examples. In: Transfer Operators, Endomorphisms, and Measurable Partitions. Lecture Notes in Mathematics, vol 2217. Springer, Cham. https://doi.org/10.1007/978-3-319-92417-5_1

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