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E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA312.SPR FCT 98404 (Browse shelf) | 1 | Available |
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QA312.SPR FCT 98137 An introduction to random currents and their applications | QA312.SPR FCT 98248 Attraction in numerical minimization | QA312.SPR FCT 98286 Modeling, dynamics, optimization and bioeconomics | QA312.SPR FCT 98404 Transfer operators, endomorphisms, and measurable partitions | QA313.SPR FCT 102513 Equidistribution and counting under equilibrium states in negative curvature and trees | QA313.SPR FCT 103630 Geometric and ergodic aspects of group actions | QA313.SPR FCT 81070 Ergodic theory |
Colocação: Online
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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