Bøger af Luis Barreira

This book comprises an impressive collection of problems that cover a variety of carefully selected topics on the core of the theory of dynamical systems. Anyone who works through the theory and problems in Part I will have acquired the background and techniques needed to do advanced studies in this area.

This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. With the exception of a few basic results from ergodic theory and the thermodynamic formalism, all the results presented include detailed proofs.

This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems. In particular, the book considers three different flavors of the thermodynamic formalism, namely nonadditive, subadditive, and almost additive, and provides a detailed discussion of some of the most significant results in the area, some of them quite recent. It also includes a discussion of the most substantial applications of these flavors of the thermodynamic formalism to dimension theory and multifractal analysis of dynamical systems.

This book offers a comprehensive overview of dimension theory of hyperbolic flows. It includes a detailed discussion of major open problems in the area.

The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner.

This rigorous yet accessible introduction to complex analysis and differential equations covers complex numbers, holomorphic functions, analytic functions, ordinary differential equations, Fourier series and applications to partial differential equations.

The main objective of this book is to give a broad uni?ed introduction to the study of dimension and recurrence inhyperbolic dynamics.

This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.