This investigation reveals conditions for semigroups to be chaotic or hypercyclic, indicating significant implications for function spaces.
To investigate conditions for strongly continuous semigroups to be chaotic or hypercyclic, we consider a strongly continuous semigroup {Tt} on a function spaceWe also consider a strongly continuous semigroup {Tt} on a function space C0([0, 1], C) or L p ([0, 1], C) expressed by Ttf (x) = q(x, t)f (e t x) with < 0, which have the relation to the solution semigroups to an initial value problem.
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Fukiko Takeo (2005) studied this question.
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