Compact Global Chaotic Attractors of Discrete Control Systems

Abstract

The paper is dedicated to the study of the problem of existence of compact global chaotic attractors of discrete control systems and to the description of its structure. We consider so called switched systems with discrete time xn+1 = fv(n)(xn), where v: Z+ → {1; 2; : : : ;m}. If m≥2 we give sufficient conditions (the family M := {f1; f2; : : : ; fm} of functions is contracting in the extended sense) for the existence of a compact global chaotic attractor. We study this problem in the framework of non-autonomous dynamical systems (cocycles)

Keywords

• Global attractor
• set-valued dynamical system
• control system
• chaotic attractor
• collage
• cocycle