Stability in terms of two measures for set difference equations in space. Issue 2 (25th January 2017)

• Record Type: Journal Article
• Authors: Slyn'ko, V. I.
• Is Part Of: Applicable analysis. Volume 96:Issue 2(2017)
• Page Start: 278
• Page End: 292
• Publication Date: 2017-01-25
• Subjects: Set difference equations -- stability in terms of two measures -- discrete dynamical systems -- mixed volume; 93D30 -- 52A39; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1126712
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : The set of trajectories for discrete dynamical systems (DDS) in the space is investigated. These sets are the solutions for difference equations in a metric space (space of nonempty convex compacts with the Hausdorff metric). On the basis of the comparison principle the general theorems on stability in terms of two measures were established. Applying the Minkowskij theory of mixed volumes, for some classes of nonlinear DDS in space the finite-dimensional comparison systems were constructed. The stability in terms of two measures and Lyapunov stability of fixed points for DDS in space were studied. The examples of studies of certain dynamical systems were given to illustrate the effectiveness of obtained results.