Chaotic behavior of <inline-formula><tex-math id="M1">$ C_0 $</tex-math></inline-formula>-semigroups of operators
Chong Yang, Denghua Zhang
Abstract
This paper characterizes the linear dynamic behaviour in $ C_0 $-semigroups. Firstly, a syndetic sequence is used to character hereditarily hypercyclic. By irregular vectors, several necessary and sufficient conditions that a $ C_0 $-semigroup is Li-Yorke chaos are obtained. Then the Li-Yorke Chaos Criterion is used to better understand the Li-Yorke Chaos. The relationship is given between discrete and continuous case. The obtained results can help to better understand the relationship between hypercyclicity and Li-Yorke chaos in $ C_0 $-semigroups.
Topics & Concepts
MathematicsOrder (exchange)Regular polygonFunction (biology)Relaxation (psychology)CombinatoricsArithmeticGeometryEvolutionary biologyPsychologyEconomicsBiologySocial psychologyFinanceStability and Controllability of Differential EquationsAdvanced Mathematical Physics ProblemsAdvanced Mathematical Modeling in Engineering