Abstract: I will discuss a number of results taken from a cross-section of my work in Dynamical Systems theory and applications. The first topics are from the ergodic theory of chaotic dynamical systems. They include relation between entropy, Lyapunov exponents and fractal dimension, statistical properties and geometry, physically relevant invariant measures, and strange attractors arising from shear-induced chaos. From there I will proceed to some applications of dynamical systems ideas, to epidemics control and computational neuroscience.
https://eta.impa.br/dl/PL010.pdf
作者首先讨论一般动力系统的三个不变量：熵，Lyapunov指数与不变测度的分数维数之间的相互关系，接着讨论混沌动力系统的统计性质（通过Markov扩张）。然后讨论奇异吸引子与SRB测度，最后讨论随机动力系统。本文还研究了动力系统在生物学中的应用：通过隔离受感染的宿主来控制流行病和大脑动力学。
相关附件
8-PL010 Young
