Some Results on the Precompactness of Orbits of Dynamical Systems.

摘要

In order to apply the invariance principle to a dynamical system on a general Banach space,it is necessary to show that positive orbits are precompact. In applications,it is often not too difficult to show that positive orbits are bounded,but this does not imply precompactness unless the underlying space is finite dimensional. Using an approach based on homeomorphic state transformations,the authors obtain certain general criteria for assuring precompactness of positive orbits. These criteria formalize and extend a number of specialized devices previously employed for this purpose. (Author)