Transfer Operators, Endomorphisms, and Measurable Partitions

Released on by Sergey Bezuglyi
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  • Transfer Operators, Endomorphisms, and Measurable Partitions Book Detail

  • Author : Sergey Bezuglyi
  • Release Date : 2018-06-21
  • Publisher : Springer
  • Genre : Mathematics
  • Pages : 167
  • ISBN 13 : 3319924176
  • File Size : 85,85 MB
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Transfer Operators, Endomorphisms, and Measurable Partitions by Sergey Bezuglyi PDF Summary

Book Description: The subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an emphasis on irreversible systems, the text presents a framework of multi-resolutions tailored for the study of endomorphisms, beginning with a systematic look at the latter. This entails a whole new set of tools, often quite different from those used for the “easier” and well-documented case of automorphisms. Among them is the construction of a family of positive operators (transfer operators), arising naturally as a dual picture to that of endomorphisms. The setting (close to one initiated by S. Karlin in the context of stochastic processes) is motivated by a number of recent applications, including wavelets, multi-resolution analyses, dissipative dynamical systems, and quantum theory. The automorphism-endomorphism relationship has parallels in operator theory, where the distinction is between unitary operators in Hilbert space and more general classes of operators such as contractions. There is also a non-commutative version: While the study of automorphisms of von Neumann algebras dates back to von Neumann, the systematic study of their endomorphisms is more recent; together with the results in the main text, the book includes a review of recent related research papers, some by the co-authors and their collaborators.

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Smooth Ergodic Theory for Endomorphisms

Smooth Ergodic Theory for Endomorphisms

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Ideal for researchers and graduate students, this volume sets out a general smooth ergodic theory for deterministic dynamical systems generated by non-invertibl