Books by Luis Barreira

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.

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.