EAN: 9783319924168

TRANSFER OPERATORS ENDOMORPHISMS AND MEASURABLE...

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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