DYNAMICS OF RELATIONS

  • Park, Jong Suh (Department of Mathematics Chungnam National University)
  • Received : 2002.06.03
  • Published : 2002.08.01

Abstract

Let X be a compact metric space and let f be a continuous relation on X. Let U be an attractor block for f and let A bean attractor determined by U. Then there exists a continuous function ${\lambda}^{-1}:X{\rightarrow}[0,1]$ such that ${\lambda}^{-1}(0)=A$, ${\lambda}^{-1}(1)=X-B(A,U)$, and $M({\lambda},f)(x)$ < ${\lambda}(x)$ for all $x{\in}B(A,U)-A$.