Chaotic or hypercyclic semigroups on a function space C0(I,ℂ) or Lp(I,ℂ)

Abstract

To investigate conditions for strongly continuous semigroups to be chaotic or hypercyclic, we consider a strongly continuous semigroup {Tt} on a function space C0([0,∞),ℂ) or Lp([0,∞),ℂ) expressed by Ttf(x)=g(x,t)f(x+t). We also consider a strongly continuous semigroup {Tt} on a function space C0([0,1],ℂ) or Lp([0,1],ℂ) expressed by Ttf(x)=q(x,t)f(eγtx) with γ<0, which have the relation to the solution semigroups to an initial value problem.