Nonuniform Hyperbolicity

Luis Barreira is a Professor of Mathematics at Instituto Superior Técnico in Lisbon. He obtained his PhD from The Pennsylvania State University in 1996, under the guidance of Yakov Pesin, with whom he co-authored the book Lyapunov Exponents and Smooth Ergodic Theory. He has also written two surveys and more than forty research papers in dynamical systems. Yakov Pesin is a Distinguished Professor of Mathematics at The Pennsylvania State University. He obtained his PhD from The Gorky State University in 1979. He is the author of three books, Dimension Theory in Dynamical Systems, Lectures on Partial Hyperbolicity and Stable Ergodicity, and, with Luis Barreira, Lyapunov Exponents and Smooth Ergodic Theory, as well as six surveys and more than seventy research papers. He is an executive editor of the journal Ergodic Theory and Dynamical Systems.

Part I. Linear Theory: 1. The concept of nonuniform hyperbolicity; 2. Lyapunov exponents for linear extensions; 3. Regularity of cocycles; 4. Methods for estimating exponents; 5. The derivative cocycle; Part II. Examples and Foundations of the Nonlinear Theory: 6. Examples of systems with hyperbolic behavior; 7. Stable manifold theory; 8. Basic properties of stable and unstable manifolds; Part III. Ergodic Theory of Smooth and SRB Measures: 9. Smooth measures; 10. Measure-theoretic entropy and Lyapunov exponents; 11. Stable ergodicity and Lyapunov exponents; 12. Geodesic flows; 13. SRB measures; Part IV. General Hyperbolic Measures: 14. Hyperbolic measures: entropy and dimension; 15. Hyperbolic measures: topological properties.