Ergodic theorems from topological and probabilistic viewpoints

Description:  Ergodic theorems are classic measure theoretical results in dynamical systems or, more precisely, ergodic theory. They state that convergence of Birkhoff averages is typical, in a measure theoretical sense. This work aims to explain how these results can be reìnterpreted in light of topology and probability theory. The first relationship is presented through a Baire category analogue of a standard version of Birkhoff's ergodic theorem (assuming ergodicity). Instead of convergence of Birkhoff averages, the topological typical behavior will be the opposite: averages do not converge in a dramatic way. If time permits, we will also explore the second relationship, which examines how the law of large numbers interacts with Birkhoff's ergodic theorem (assuming ergodicity). Date:  2019-10-16 Start Time:   11:30 Speaker:  Lucas Amorim (UC|UP PhD student) Institution:  Universidade do Porto Place:  Sala 004, UP Math. Dept. See more:   <Main>   <UC|UP MATH PhD Program>