Skip to main content
Top

2002 | OriginalPaper | Chapter

Dynamical Systems: Basic Theory

Authors : George R. Sell, Yuncheng You

Published in: Dynamics of Evolutionary Equations

Publisher: Springer New York

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

The basic concept underlying the study of dynamics in infinite dimensional spaces is that of a semiflow, or as it is sometimes called, a semigroup. This semiflow is a time-dependent action on the ambient space, which we assume to be a complete metric space W, for example, a Banach space or a Fréchet space. One should think of the semiflow as a mechanism for describing the solutions of an underlying evolutionary equation. This evolutionary equation is oftentimes the abstract formulation of a given partial differential equation or, sometimes, an ordinary differential equation with time delays. In this chapter we will examine some basic properties of semiflows. Our principal objective is to describe the longtime dynamics in terms of the invariant sets, the limit sets, and the attractors of the semiflow. A comprehensive theory of global attractors is included here. Later in this volume, we will develop the connections between the semiflow and the underlying evolutionary equation.

Metadata
Title
Dynamical Systems: Basic Theory
Authors
George R. Sell
Yuncheng You
Copyright Year
2002
Publisher
Springer New York
DOI
https://doi.org/10.1007/978-1-4757-5037-9_2

Premium Partner