Discrete Dynamics in Nature and Society
Volume 1 (1998), Issue 4, Pages 307-313
doi:10.1155/S1026022697000290
Absorbers: Definitions, properties and applications
Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
Received 12 January 1997; Revised 26 March 1997
Copyright © 1998 G. Belitskii. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Roughly speaking, the absorber is a set, which includes, after finite number of initial states, each trajectory of a transformation of space into itself. This paper deals with the exact definition of absorbers for linear operators, the study of the properties, the applications to “classical” dynamics and to solvability of operator equations. It is expected that the description of the structure of absorbers will add new insights to the recent discussion of nature and content of notion of attractiveness for nonlinear dynamics.