Quantitative aspects of dynamical systems

动力系统为许多应用科学提供了基本的模型和强大的工具。由于动力学的范围不断扩大，定量和计算方面现在构成了一个充满活力的研究领域。在这个领域内，拟议的研究计划将

Dynamical systems provide fundamental models and powerful tools for many applied sciences. Due to the ever-expanding scope of dynamics, quantitative and computational aspects now constitute a vibrant research area. Within this area, the proposed research program will (i) develop a comprehensive theory of Benford's Law in the context of dynamical systems; (Benford's Law is a well-documented empirical observation stating a particular distribution of significant digits in numerical data; while its important and surprising implications, e.g. in numerical analysis and statistics, have recently attracted a lot of attention, many natural mathematical questions concerning Benford's Law are still open.) (ii) study finite data sets and dynamically relevant measures by means of a novel approach to constrained quantization; (iii) introduce and study fundamental concepts and tools for finite-time dynamics, e.g. hyperbolicity and spectrum, and apply them to nonautonomous bifurcations and driven billiards. Overall, the program will bring about a deepened understanding of important quantitative aspects of dynamical systems, leading in turn to more reliable statistical tests and plausibility checks (e.g. for accounting and election fraud) as well as improved numerical procedures wherever dynamical systems serve as models for real-world processes.