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.