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Ergodic Theory and Applications

Bryna Kra, Robert A. Meyers (Herausgeber)

Buch | Hardcover

320 Seiten

2012
Springer, Berlin (Verlag)
9781441993496 (ISBN)

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Dynamical systems is the study of systems that evolve with time, and ergodic theory is the branch of dynamics that studies the statistical and qualitative behavior of measurable actions on a measure space. The problems, results, and techniques of Ergodic theory lie at the intersection of many areas of mathematics, including smooth dynamics, statistical mechanics, probability, harmonic analysis, and group actions. Recently, ergodic theory has seen a burst of activity in which ergodic theory and its techniques have been imported into combinatorics, number theory, and geometry. This volume, which contains authoritative entries from the Encyclopedia of Complexity and Systems Science, begins with an overview of the basic objects in ergodic theory, including recurrence, convergence theorems, mixing, and entropy, and continues with an overview of the recent connections with other fields. These interactions include traditional areas such as topological, smooth, and symbolic dynamics, but also include areas traditionally outside the scope of ergodic theory, such as fractal geometry, number theory, and combinatorics.

Robert A. Meyers obtained his Ph.D. in Chemistry at the University of California at Los Angeles. He was a post-doctoral fellow at the California Institute of Technology and has more than 17 patents, 50 technical papers and 12 books to his name. As Editor-in-Chief he conceived and edited several ambitious multivolume reference works.

IntroductionMeasure Preserving SystemsBasic Examples and ConstructionsErgodic TheoremsRecurrenceMixing PropertiesIsomorphism TheoryJoiningsRigiditySmooth Ergodic TheorySymbolic DynamicsTopological DynamicsNon-singular TransformationsEntropyPressure and Equilibriums StatesChaosFractal GeometryErgodic Theory on Homogeneous Spaces and Metric Number Theory

Sprache	englisch
Maße	210 x 279 mm
Einbandart	gebunden
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Applications of ergodic theory • Dynamical Systems • Dynamical systems reference • ergodic theory • Ergodic theory and Convergence • Ergodic theory and Entropy • Ergodic theory and Fractal geometry • Ergodic theory and Mixing • Ergodic theory and Recurrence • Ergodic theory reference • Ergodic theory review
ISBN-13	9781441993496 / 9781441993496
Zustand	Neuware