| 书目名称 | Ergodic Dynamics | | 副标题 | From Basic Theory to | | 编辑 | Jane Hawkins | | 视频video | | | 概述 | Offers an accessible introduction to the dynamics of ergodic systems.Unifies topics across ergodic theory, topological dynamics, complex dynamics, and dynamical systems.Explores real-world application | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | .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 e | | 出版日期 | Textbook 2021 | | 关键词 | Ergodic theory textbook; Dynamical systems textbook; Dynamics of ergodic systems; Complex dynamics; Topo | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-59242-4 | | isbn_softcover | 978-3-030-59244-8 | | isbn_ebook | 978-3-030-59242-4Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer Nature Switzerland AG 2021 |
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发表于 2025-3-21 18:24:07
