Dimension and Recurrence in Hyperbolic Dynamics (Progress in Mathematics, 272, Band 272) - Hardcover

Barreira, Luis

Hardcover

ISBN 10: 3764388811 ISBN 13: 9783764388812

Verlag: Birkhäuser, 2008

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

Luis Barreira is a Full Professor of Mathematics at Instituto Superior Técnico, Lisbon and a member of the Center for Mathematical Analysis, Geometry, and Dynamical Systems. He obtained his PhD from the Pennsylvania State University in 1996. In 2007 he has been awarded the Gulbenkian Science Prize.   Claudia Valls is an Invited Assistant Professor at Instituto Superior Técnico, Lisbon and a Postdoctoral Fellow at the Center for Mathematical Analysis, Geometry, and Dynamical Systems, of which she is also a member. She obtained her PhD from the Universitat de Barcelona in 1999.

Von der hinteren Coverseite

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.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2008
• Sprache: Englisch
• ISBN 10: 3764388811
• ISBN 13: 9783764388812
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 314
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland