Buch, Englisch, Band 272, 300 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 647 g
Reihe: Progress in Mathematics
Buch, Englisch, Band 272, 300 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 647 g
Reihe: Progress in Mathematics
ISBN: 978-3-7643-8881-2
Verlag: Springer
The main objective of this book is to give a broad uni?ed introduction to the study of dimension and recurrence inhyperbolic dynamics. It includes a disc- sion of the foundations, main results, and main techniques in the rich interplay of fourmain 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. This includes topics on irregular sets, var- tional principles, applications to number theory, measures of maximal dimension, multifractal rigidity, and quantitative recurrence. The book isdirected to researchersas well as graduate students whowish to have a global view of the theory together with a working knowledgeof its main techniques. It can also be used as a basis for graduatecourses in dimension theory of dynamical systems, multifractal analysis (together with a discussion of several special topics), and pointwise dimension and recurrence in hyperbolic dynamics. I hope that the book may serve as a fast entry point to this exciting and active ?eld of research, and also that it may lead to further developments.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
- Mathematik | Informatik Mathematik Topologie Analytische Topologie
- Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
Weitere Infos & Material
Basic Notions.- Basic Notions.- Dimension Theory.- Dimension Theory and Thermodynamic Formalism.- Repellers and Hyperbolic Sets.- Measures of Maximal Dimension.- Multifractal Analysis: Core Theory.- Multifractal Analysis of Equilibrium Measures.- General Concept of Multifractal Analysis.- Dimension of Irregular Sets.- Variational Principles in Multifractal Analysis.- Multifractal Analysis: Further Developments.- Multidimensional Spectra and Number Theory.- Multifractal Rigidity.- Hyperbolic Sets: Past and Future.- Hyperbolicity and Recurrence.- Pointwise Dimension for Hyperbolic Dynamics.- Product Structure of Hyperbolic Measures.- Quantitative Recurrence and Dimension Theory.
