Evolutionary Systems and Weighted Translation Operators

主要研究者提出了在线性半群和无限维动力系统的渐近理论的交叉点上解决一些描述演化系统和半流在Banach空间上的渐近性质（二分性、双曲性、Lyapunov指数）的问题。主要的技术工具是在描述中使用加权平移算子的半群。这种技术将允许人们从一个相当意想不到的角度来看待经典的李亚普诺夫定理。这项工作植根于对过程稳定性的分析。这些过程通常用微分方程来描述，稳定性是通过分析解的渐近或大时间行为来确定的。这些方程的解自然地存在于被称为巴拿赫空间的抽象结构中，稳定性问题的研究可以用度量或范数来表述。这样就可以有效地利用算子理论技术来研究动力系统的稳定性。该理论在发电机理论和化学反应器动力学中都有应用。＊＊＊

9400518 Latushkin The Principal Investigator proposes to solve some problems at the intersection of the asymptotic theory of linear semigroups and infinite dimensional dynamical systems to describe the asymptotic properties (dichotomy, hyberbolicity, Lyapunov exponents) of evolutionary systems and semiflows on Banach spaces. The main technical tool is to involve for this description the semigroups of weighted translation operators. This technique would allow one to view the classical Lyapunov theorems in a fairly unexpected perspective. This work has its roots in the analysis of stability of processes. These processes are frequently described by differential equations and the stability is determined by an analysis of the asymptotic or large time behavior of the solutions. The solutions of these equations live naturally in abstract structures called Banach spaces and the study of stability questions can be formulated in terms of a metric or norm. In this way the techniques of operator theory can be used effectively to study stability of dynamical systems. The theory has applications in dynamo theory and the dynamics of chemical reactors. ***