Transfer Operators Endomorphisms And Measurable Partitions

Author : Sergey Bezuglyi,Palle E. T. Jorgensen
Publisher : Springer
Page : 162 pages
File Size : 45,6 Mb
Release : 2018-06-21
Category : Mathematics
ISBN : 9783319924175

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Transfer Operators, Endomorphisms, and Measurable Partitions by Sergey Bezuglyi,Palle E. T. Jorgensen Pdf

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.

Author : Daniel Alpay,Ronen Peretz,David Shoikhet,Mihaela B. Vajiac
Publisher : Springer Nature
Page : 389 pages
File Size : 45,9 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030764739

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New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative by Daniel Alpay,Ronen Peretz,David Shoikhet,Mihaela B. Vajiac Pdf

This volume presents selected contributions from experts gathered at Chapman University for a conference held in November 2019 on new directions in function theory. The papers, written by leading researchers in the field, relate to hypercomplex analysis, Schur analysis and de Branges spaces, new aspects of classical function theory, and infinite dimensional analysis. Signal processing constitutes a strong presence in several of the papers.A second volume in this series of conferences, this book will appeal to mathematicians interested in learning about new fields of development in function theory.

Author : Daniel Alpay,Mihaela B. Vajiac
Publisher : Springer
Page : 316 pages
File Size : 53,8 Mb
Release : 2019-08-08
Category : Mathematics
ISBN : 9783030184841

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Linear Systems, Signal Processing and Hypercomplex Analysis by Daniel Alpay,Mihaela B. Vajiac Pdf

This volume includes contributions originating from a conference held at Chapman University during November 14-19, 2017. It presents original research by experts in signal processing, linear systems, operator theory, complex and hypercomplex analysis and related topics.

Author : Mariusz Urbański,Mario Roy,Sara Munday
Publisher : Walter de Gruyter GmbH & Co KG
Page : 487 pages
File Size : 44,9 Mb
Release : 2023-09-05
Category : Mathematics
ISBN : 9783110769890

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Analytic Endomorphisms of the Riemann Sphere by Mariusz Urbański,Mario Roy,Sara Munday Pdf

Complex dynamics is one of the most fascinating subjects of study and research in mathematics. This third volume in the series entitled Non-Invertible Dynamical Systems not only examines topological and analytical properties of the iteration of rational functions on the Riemann sphere (in particular, the Fatou and Julia sets) but also focuses on thermodynamic, ergodic and fractal properties of these functions (notably, equilibrium states, Bowen's formula and Sullivan’s conformal measures). This volume builds on the first two volumes in the series while simultaneously developing some methods and techniques specific to rational functions.

Author : Min Qian,Jian-Sheng Xie,Shu Zhu
Publisher : Springer
Page : 292 pages
File Size : 41,5 Mb
Release : 2009-07-07
Category : Mathematics
ISBN : 9783642019548

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Smooth Ergodic Theory for Endomorphisms by Min Qian,Jian-Sheng Xie,Shu Zhu Pdf

Ideal for researchers and graduate students, this volume sets out a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms. Its focus is on the relations between entropy, Lyapunov exponents and dimensions.

Author : Feliks Przytycki,Mariusz Urbański
Publisher : Cambridge University Press
Page : 365 pages
File Size : 47,9 Mb
Release : 2010-05-06
Category : Mathematics
ISBN : 9780521438001

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Conformal Fractals by Feliks Przytycki,Mariusz Urbański Pdf

A one-stop introduction to the methods of ergodic theory applied to holomorphic iteration that is ideal for graduate courses.

Author : Anonim
Publisher : Unknown
Page : 1884 pages
File Size : 45,9 Mb
Release : 2005
Category : Mathematics
ISBN : UVA:X006195258

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Mathematical Reviews by Anonim Pdf

Author : Jane Hawkins
Publisher : Springer Nature
Page : 340 pages
File Size : 40,7 Mb
Release : 2021-01-28
Category : Mathematics
ISBN : 9783030592424

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Ergodic Dynamics by Jane Hawkins Pdf

This textbook provides a broad introduction to the fields of dynamical systems and ergodic theory. Motivated by examples throughout, the author offers readers an approachable entry-point to the dynamics of ergodic systems. Modern and classical applications complement the theory on topics ranging from financial fraud to virus dynamics, offering numerous avenues for further inquiry. Starting with several simple examples of dynamical systems, the book begins by establishing the basics of measurable dynamical systems, attractors, and the ergodic theorems. From here, chapters are modular and can be selected according to interest. Highlights include the Perron–Frobenius theorem, which is presented with proof and applications that include Google PageRank. An in-depth exploration of invariant measures includes ratio sets and type III measurable dynamical systems using the von Neumann factor classification. Topological and measure theoretic entropy are illustrated and compared in detail, with an algorithmic application of entropy used to study the papillomavirus genome. A chapter on complex dynamics introduces Julia sets and proves their ergodicity for certain maps. Cellular automata are explored as a series of case studies in one and two dimensions, including Conway’s Game of Life and latent infections of HIV. Other chapters discuss mixing properties, shift spaces, and toral automorphisms. Ergodic Dynamics unifies topics across ergodic theory, topological dynamics, complex dynamics, and dynamical systems, offering an accessible introduction to the area. Readers across pure and applied mathematics will appreciate the rich illustration of the theory through examples, real-world connections, and vivid color graphics. A solid grounding in measure theory, topology, and complex analysis is assumed; appendices provide a brief review of the essentials from measure theory, functional analysis, and probability.

Author : Palle Jorgensen,James Tian
Publisher : World Scientific
Page : 253 pages
File Size : 42,6 Mb
Release : 2021-01-15
Category : Mathematics
ISBN : 9789811225796

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Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory by Palle Jorgensen,James Tian Pdf

The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.

Author : Jean-Pierre Françoise,Gregory L. Naber,Tsou Sheung Tsun
Publisher : Academic Press
Page : 792 pages
File Size : 55,6 Mb
Release : 2006-06-06
Category : Science
ISBN : 0125126603

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Encyclopedia of Mathematical Physics by Jean-Pierre Françoise,Gregory L. Naber,Tsou Sheung Tsun Pdf

The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originating from work in mathematical physics by providing them with focused high quality background information. Editorial Board: Jean-Pierre Françoise, Université Pierre et Marie Curie, Paris, FranceGregory L. Naber, Drexel University, Philadelphia, PA, USATsou Sheung Tsun, University of Oxford, UK Also available online via ScienceDirect (2006) - featuring extensive browsing, searching, and internal cross-referencing between articles in the work, plus dynamic linking to journal articles and abstract databases, making navigation flexible and easy. For more information, pricing options and availability visit www.info.sciencedirect.com.

Author : Palle E. T. Jorgensen
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 46,6 Mb
Release : 2007-10-17
Category : Mathematics
ISBN : 9780387330822

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Analysis and Probability by Palle E. T. Jorgensen Pdf

Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to mathematicians and operator theory to engineers Fills a gap in the literature

Author : Paul R. Halmos
Publisher : Courier Dover Publications
Page : 113 pages
File Size : 52,6 Mb
Release : 2017-12-13
Category : Mathematics
ISBN : 9780486814896

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Lectures on Ergodic Theory by Paul R. Halmos Pdf

This concise classic by Paul R. Halmos, a well-known master of mathematical exposition, has served as a basic introduction to aspects of ergodic theory since its first publication in 1956. "The book is written in the pleasant, relaxed, and clear style usually associated with the author," noted the Bulletin of the American Mathematical Society, adding, "The material is organized very well and painlessly presented." Suitable for advanced undergraduates and graduate students in mathematics, the treatment covers recurrence, mean and pointwise convergence, ergodic theorem, measure algebras, and automorphisms of compact groups. Additional topics include weak topology and approximation, uniform topology and approximation, invariant measures, unsolved problems, and other subjects.

Author : Jorgensen Palle,Tian Feng
Publisher : World Scientific
Page : 564 pages
File Size : 45,5 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9789813202146

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Non-commutative Analysis by Jorgensen Palle,Tian Feng Pdf

The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.) A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras. The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

Author : Emily Riehl
Publisher : Courier Dover Publications
Page : 272 pages
File Size : 45,9 Mb
Release : 2017-03-09
Category : Mathematics
ISBN : 9780486820804

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Category Theory in Context by Emily Riehl Pdf

Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Author : Volodymyr Nekrashevych
Publisher : American Mathematical Society
Page : 248 pages
File Size : 41,6 Mb
Release : 2024-04-05
Category : Mathematics
ISBN : 9781470476915

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Self-Similar Groups by Volodymyr Nekrashevych Pdf

Self-similar groups (groups generated by automata) appeared initially as examples of groups that are easy to define but that enjoy exotic properties like nontrivial torsion, intermediate growth, etc. The book studies the self-similarity phenomenon in group theory and shows its intimate relation with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. The relation is established through the notions of the iterated monodromy group and the limit space, which are the central topics of the book. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. It is shown in particular how Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties appear now not just as isolated examples but as naturally defined iterated monodromy groups of rational functions. The book is intended to be accessible to a wide mathematical readership, including graduate students interested in group theory and dynamical systems.