TY - BOOK ID - 219468 TI - Dimension and recurrence in hyperbolic dynamics PY - 2008 SN - 1281872431 9786611872434 376438882X 3764388811 PB - Basel : [London : Birkhàˆuser ; Springer, distributor], DB - UniCat KW - Differentiable dynamical systems. KW - Hyperbolic groups. KW - Dimension theory (Topology) KW - Topology KW - Group theory KW - Differential dynamical systems KW - Dynamical systems, Differentiable KW - Dynamics, Differentiable KW - Differential equations KW - Global analysis (Mathematics) KW - Topological dynamics KW - Cell aggregation KW - Global analysis (Mathematics). KW - Dynamical Systems and Ergodic Theory. KW - Manifolds and Cell Complexes (incl. Diff.Topology). KW - Analysis. KW - Mathematics. KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Aggregation, Cell KW - Cell patterning KW - Cell interaction KW - Microbial aggregation KW - Dynamics. KW - Ergodic theory. KW - Manifolds (Mathematics). KW - Complex manifolds. KW - Mathematical analysis. KW - Analysis (Mathematics). KW - 517.1 Mathematical analysis KW - Mathematical analysis KW - Analytic spaces KW - Manifolds (Mathematics) KW - Geometry, Differential KW - Ergodic transformations KW - Continuous groups KW - Mathematical physics KW - Measure theory KW - Transformations (Mathematics) KW - Dynamical systems KW - Kinetics KW - Mathematics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Physics KW - Statics UR - https://www.unicat.be/uniCat?func=search&query=sysid:219468 AB - The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. More than half of the material appears here for the first time in book form, describing many recent developments in the area such as topics on irregular sets, variational principles, applications to number theory, measures of maximal dimension, multifractal nonrigidity, and quantitative recurrence. All the results are included with detailed proofs, many of them simplified or rewritten on purpose for the book. The text is self-contained and directed to researchers as well as graduate students that wish to have a global view of the theory together with a working knowledge of its main techniques. It will also be useful as as basis for graduate courses in dimension theory of dynamical systems, multifractal analysis, and pointwise dimension and recurrence in hyperbolic dynamics. ER -