Rich with examples, applications and over 400 exercises, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. It requires few prerequisites, beginning with elementary material suitable for undergraduate students and gradually building up to more sophisticated topics.
Rich with examples, applications and over 400 exercises, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. It requires few prerequisites, beginning with elementary material suitable for undergraduate students and gradually building up to more sophisticated topics.
Marcelo Viana is Professor of Mathematics at the Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, and a leading research expert in ergodic theory and dynamical systems. He has served in several academic organizations, such as the International Mathematical Union (Vice President, 2011¿2014), the Brazilian Mathematical Society (President, 2013¿2015), the Latin American Mathematical Union (Scientific Coordinator, 2001¿2008) and the newly founded Mathematical Council of the Americas. He is also a member of the academies of science of Brazil, Portugal, Chile and the Developing World, and he has received several academic distinctions, including the Grand Croix of Scientific Merit, granted by the President of Brazil, in 2000, and the Ramanujan Prize of ICTP and IMU in 2005. He was an Invited Speaker at the International Congress of Mathematicians in Zurich (1994), a Plenary Speaker at the International Congress of Mathematical Physics (1994), and a Plenary Speaker at the ICM in Berlin (1998). To date, he has supervised thirty-two doctoral theses. Currently, he leads the organization of the ICM 2018 in Rio de Janeiro, and he is also involved in initiatives to improve mathematical education in his country.
Inhaltsangabe
Preface 1. Recurrence 2. Existence of invariant measures 3. Ergodic theorems 4. Ergodicity 5. Ergodic decomposition 6. Unique ergodicity 7. Correlations 8. Equivalent systems 9. Entropy 10. Variational principle 11. Expanding maps 12. Thermodynamical formalism Appendix. Topics of measure theory, topology and analysis Hints or solutions for selected exercises References Index.
