Linear dynamics of semigroups generated by differential operators
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Other documents of the author: Conejero, J. Alberto; Lizama, Carlos; murillo arcila, marina; Peris, A.
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Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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INVESTIGACIONMetadata
Title
Linear dynamics of semigroups generated by differential operatorsDate
2017Publisher
De GruyterISSN
2391-5455Type
info:eu-repo/semantics/articlePublisher version
https://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0065/math-2017-0 ...Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
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 ... [+]
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. [-]
Is part of
Open Math. 2017; 15Investigation project
FEDER/MTM201675963-P ; CONICYT under FONDECYT/1140258 ; CONICYT-PIA-Anillo/ACT1416Rights
info:eu-repo/semantics/openAccess
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