Na próxima semana iniciaremos o semestre letivo na UFF com um minicurso proferido por Odylo Costa sobre Emergência em Sistemas Dinâmicos (veja o resumo abaixo).
Os dois seminários irão ocorrer na terça e na quinta (10 e 12 de março) às 16h na sala 401 da Pós-Graduação em Matemática da UFF.
Title: Emergence in dynamical systems: quantifying non-ergodicity
Abstract: Emergence is a quantitative way to measure how far a dynamical system is from being ergodic. Roughly speaking, it counts how many different statistical behaviors are needed to describe typical orbits at a given scale. In this minicourse, we recall the basic definitions and then focus on two complementary viewpoints. In the first meeting, we discuss metric and topological emergence and their relation with ergodic decompositions, highlighting the example of Berger and Bochi [1] of a smooth conservative diffeomorphism with zero entropy but high emergence. In the second meeting, we introduce pointwise emergence and its link to historical behavior (the failure of time averages). We then present the dissipative example of Kiriki, Nakano, and Soma [2] with high emergence, and discuss the dynamical mechanisms that produce large pointwise emergence.
References:
[1] P. Berger and J. Bochi, On emergence and complexity of ergodic decompositions, Advances in Mathematics 390 (2021), 107904.
[2] S. Kiriki, Y. Nakano, and T. Soma, Emergence via non-existence of average, Ergodic Theory and Dynamical Systems (2022).