Linear dynamics of semigroups generated by differential operators

• Autorzy: J. Alberto Conejero , Carlos Lizama , Marina Murillo-Arcila , Alfredo Peris
• Języki publikacji: EN

Abstrakty

EN

During the last years, several notions have been introduced for describing the dynamical behavior of linear operators on infinite-dimensional spaces, such as hypercyclicity, chaos in the sense of Devaney, chaos in the sense of Li-Yorke, subchaos, mixing and weakly mixing properties, and frequent hypercyclicity, among others. These notions have been extended, as far as possible, to the setting of C0-semigroups of linear and continuous operators. We will review some of these notions and we will discuss basic properties of the dynamics of C0-semigroups. We will also study in detail the dynamics of the translation C0-semigroup on weighted spaces of integrable functions and of continuous functions vanishing at infinity. Using the comparison lemma, these results can be transferred to the solution C0-semigroups of some partial differential equations. Additionally, we will also visit the chaos for infinite systems of ordinary differential equations, that can be of interest for representing birth-and-death process or car-following traffic models.

Słowa kluczowe

EN

Hypercyclicity; Topological transitivity; Topologically mixing property; Devaney chaos; C0-semigroups

Kategorie tematyczne

• 47A16: Cyclic vectors, hypercyclic and chaotic operators

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 745-767

Daty

wydano

2017-01-01

otrzymano

2017-03-31

zaakceptowano

2017-04-17

online

2017-06-09

Twórcy

autor

J. Alberto Conejero

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autor

Carlos Lizama

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autor

Marina Murillo-Arcila

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autor

Alfredo Peris

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Identyfikatory

DOI

10.1515/math-2017-0065