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Topological dynamics. --- Dynamics, Topological --- Differentiable dynamical systems
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This book presents the development and application of some topological methods in the analysis of data coming from 3D dynamical systems (or related objects). The aim is to emphasize the scope and limitations of the methods, what they provide and what they do not provide. Braid theory, the topology of surface homeomorphisms, data analysis and the reconstruction of phase-space dynamics are thoroughly addressed.
Topological dynamics. --- Dimension theory (Topology) --- Topology --- Dynamics, Topological --- Differentiable dynamical systems
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This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon-McMillan-Breiman Theorem, the Ornstein-Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses symbolic extension entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research.
Topological entropy --- Topological dynamics --- Dynamics, Topological --- Differentiable dynamical systems --- Entropy, Topological
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This monograph presents developments in the abstract theory of topological dynamics, concentrating on the internal structure of minimal flows (actions of groups on compact Hausdorff spaces for which every orbit is dense) and their homomorphisms (continuous equivariant maps). Various classes of minimal flows (equicontinuous, distal, point distal) are intensively studied, and a general structure theorem is obtained. Another theme is the ``universal'' approach - entire classes of minimal flows are studied, rather than flows in isolation. This leads to the consideration of disjointness of flows,
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Semigroups. --- Topological dynamics. --- Dynamics, Topological --- Differentiable dynamical systems --- Group theory --- Dinàmica topològica --- Semigrups
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Topology --- Topological dynamics --- Congresses --- 515.1 --- -Dynamics, Topological --- Differentiable dynamical systems --- Congresses. --- -Topology --- 515.1 Topology --- -515.1 Topology --- Dynamics, Topological --- Dynamique différentiable --- Systèmes dynamiques --- Dynamique différentiable --- Systèmes dynamiques --- Topological dynamics - Congresses --- Theorie ergodique
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This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups.
Ergodic theory. --- Topological dynamics. --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Ergodic theory --- Topological dynamics --- Dynamics, Topological --- Differentiable dynamical systems
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Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory.
Topological dynamics. --- Ergodic theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamics, Topological --- Differentiable dynamical systems
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The study of geodesic flows on homogenous spaces is an area of research that has yielded some fascinating developments. This book, first published in 2000, focuses on many of these, and one of its highlights is an elementary and complete proof (due to Margulis and Dani) of Oppenheim's conjecture. Also included here: an exposition of Ratner's work on Raghunathan's conjectures; a complete proof of the Howe-Moore vanishing theorem for general semisimple Lie groups; a new treatment of Mautner's result on the geodesic flow of a Riemannian symmetric space; Mozes' result about mixing of all orders and the asymptotic distribution of lattice points in the hyperbolic plane; Ledrappier's example of a mixing action which is not a mixing of all orders. The treatment is as self-contained and elementary as possible. It should appeal to graduate students and researchers interested in dynamical systems, harmonic analysis, differential geometry, Lie theory and number theory.
Ergodic theory. --- Topological dynamics. --- Dynamics, Topological --- Differentiable dynamical systems --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics)
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