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. All the results are included with detailed proofs, many of them simplified or rewritten on purpose for the book. The text is self-contained. Pragmatic introduction to the study of dimension and recurrence in hyperbolic dynamics, traveling firmly but also rigorously from the basics to the frontiers of research in the area More than half of the material appears here for the first time in book form, with the description of many recent developments in the area, on topics such as irregular sets, variational principles, applications to number theory, etc. INDICE: Preface.- Introduction.- Basic Notions.- I. Dimension Theory.- Dimension Theory and Thermodynamic Formalism.- Repellers and Hyperbolic Sets.- Measures of Maximal Dimension.- II. Multifractal Analysis: Core Theory.- Multifractal Analysis of Equilibrium Measures.- General Concept of Multifractal Analysis.- Dimension of Irregular Sets.- Variational Principles in Multifractal Analysis.- III. Multifractal Analysis: Further Developments.- Multidimensional Spectra and Number Theory.- Multifractal Rigidity.- Hyperbolic Sets: Past and Future.- IV. Hyperbolicity and Recurrence.- Pointwise Dimension for Hyperbolic Dynamics.- Product Structure of Hyperbolic Measures.- Quantitative Recurrence and Dimension Theory.
- ISBN: 978-3-7643-8881-2
- Editorial: Birkhaüser
- Encuadernacion: Cartoné
- Páginas: 310
- Fecha Publicación: 01/07/2008
- Nº Volúmenes: 1
- Idioma: Inglés