001433703 000__ 04464cam\a2200541\i\4500
001433703 001__ 1433703
001433703 003__ OCoLC
001433703 005__ 20230309003649.0
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001433703 008__ 210206s2021\\\\sz\a\\\\ob\\\\001\0\eng\d
001433703 019__ $$a1235871754
001433703 020__ $$a3030592421$$q(electronic book)
001433703 020__ $$a9783030592424$$q(electronic bk.)
001433703 020__ $$z3030592413
001433703 020__ $$z9783030592417
001433703 0247_ $$a10.1007/978-3-030-59242-4$$2doi
001433703 035__ $$aSP(OCoLC)1236261537
001433703 040__ $$aEBLCP$$beng$$erda$$epn$$cEBLCP$$dGW5XE$$dYDX$$dOCLCO$$dN$T$$dOCLCF$$dUKAHL$$dSFB$$dOCLCO$$dOCLCQ$$dOCLCO$$dOCLCQ
001433703 049__ $$aISEA
001433703 050_4 $$aQA614.8
001433703 08204 $$a515.48$$223
001433703 1001_ $$aHawkins, Jane,$$d1954-$$eauthor.
001433703 24510 $$aErgodic dynamics :$$bfrom basic theory to applications /$$cJane Hawkins.
001433703 264_1 $$aCham, Switzerland :$$bSpringer,$$c[2021]
001433703 300__ $$a1 online resource :$$billustrations (some color)
001433703 336__ $$atext$$btxt$$2rdacontent
001433703 337__ $$acomputer$$bc$$2rdamedia
001433703 338__ $$aonline resource$$bcr$$2rdacarrier
001433703 4901_ $$aGraduate texts in mathematics ;$$v289
001433703 504__ $$aIncludes bibliographical references and index.
001433703 5050_ $$aThe simplest examples -- Dynamical Properties of Measurable Transformations -- Attractors in Dynamical Systems -- Ergodic Theorems -- Mixing Properties of Dynamical Systems -- Shift Spaces -- Perron-Frobenius Theorem and Some Applications -- Invariant Measures -- No equivalent invariant measures: Type III maps -- Dynamics of Automorphisms of the Torus and Other Groups -- An Introduction to Entropy -- Complex Dynamics -- Maximal Entropy Measures on Julia Sets and a Computer Algorithm -- Cellular Automata -- Appendix A. Measures on Topological Spaces -- Appendix B. Integration and Hilbert Spaces -- Appendix C. Connections to Probability Theory.
001433703 506__ $$aAccess limited to authorized users.
001433703 520__ $$aThis 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 PerronFrobenius 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 Conways 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.
001433703 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed March 10, 2021).
001433703 650_0 $$aDifferentiable dynamical systems.
001433703 650_0 $$aErgodic theory.
001433703 650_6 $$aDynamique différentiable.
001433703 650_6 $$aThéorie ergodique.
001433703 655_0 $$aElectronic books.
001433703 77608 $$iPrint version:$$z9783030592417
001433703 830_0 $$aGraduate texts in mathematics ;$$v289.
001433703 852__ $$bebk
001433703 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-59242-4$$zOnline Access$$91397441.1
001433703 909CO $$ooai:library.usi.edu:1433703$$pGLOBAL_SET
001433703 980__ $$aBIB
001433703 980__ $$aEBOOK
001433703 982__ $$aEbook
001433703 983__ $$aOnline
001433703 994__ $$a92$$bISE