Distributional Chaoticity of C0-Semigroup on a Frechet Space

Abstract

This paper is mainly concerned with distributional chaos and the principal measure of C 0 -semigroups on a Frechet space. New definitions of strong irregular (semi-irregular) vectors are given. It is proved that if C 0 -semigroup T has strong irregular vectors, then T is distributional chaos in a sequence, and the principal measure μ p ( T ) is 1. Moreover, T is distributional chaos equivalent to that operator T t   is distributional chaos for every ∀ t > 0 .

Keywords

• Frechet spaces
• C0-semigroups
• distributional chaos
• strong irregular vector