Limit sets and prolongations in topological dynamics

Bae, Jong Sook; Choi, Sung Kyu; Park, Jong Suh

doi:10.1016/0022-0396(86)90079-3

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Introduction2

Set-valued Dynamical Systems1

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2022

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Cited by 3 publications

(3 citation statements)

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“…In [3], Bae, Choi and Park studied limit sets and prolongational sets in topological dynamics. Next remark is immediately proved from the definitions.…”

Section: Set-valued Dynamical Systemsmentioning

confidence: 99%

See 1 more Smart Citation

A Topological Characterization of ω-Limit Sets on Dynamical Systems

Chu¹,

Kim²,

Park

2014

Journal of the Chungcheong Mathematical Society

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“…In [3], Bae, Choi and Park studied limit sets and prolongational sets in topological dynamics. Next remark is immediately proved from the definitions.…”

Section: Set-valued Dynamical Systemsmentioning

confidence: 99%

“…The notion is a very strong tool to understand important theories in the several fields of Mathematics and generates many results about the induced concepts, for example, chain transitive, chain recurrence, shadowing property and so on. See [2,3,4,5,15,17,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

A Topological Characterization of ω-Limit Sets on Dynamical Systems

Chu¹,

Kim²,

Park

2014

Journal of the Chungcheong Mathematical Society

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“…The notions of prolongations play an important role in studying dynamical systems [2,3,14]. In [15], Ura showed that the concept was closely related to the one of stabilities in the sense of Liapunov.…”

Section: Introductionmentioning

confidence: 99%

Some Remarks on Chain Prolongations in Dynamical Systems

Chu¹,

Kim²,

Park³

2013

Journal of the Chungcheong Mathematical Society

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P- Omega Limit Set in Random Dynamical Systems

Alkhrayfawee

Kadhim

Albukhuttar

2022

J. Phys.: Conf. Ser.

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The primary objective of this work is to investigate the idea of P-omega limit sets in a random dynamical system, where P might refer to any replete semi group in the time-space (considered a locally compact group with Harr measure). Within the context of a random dynamical system, the ideas of P-trajectory and P-invariant random sets are discussed; moreover, several fundamental features connected to these notions are looked into. The concept of a P-omega limit set of random sets in a random dynamical system is established, and several fundamental aspects are shown using mathematical proofs. In addition to this, the connection that exists between the P-trajectory and the P-omega limit set is shown.

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Limit sets and prolongations in topological dynamics

Cited by 3 publications

References 2 publications

A Topological Characterization of ω-Limit Sets on Dynamical Systems

A Topological Characterization of ω-Limit Sets on Dynamical Systems

Some Remarks on Chain Prolongations in Dynamical Systems

P- Omega Limit Set in Random Dynamical Systems

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Limit sets and prolongations in topological dynamics

Cited by 3 publications

References 2 publications

A Topological Characterization of ­ω-Limit Sets on Dynamical Systems

A Topological Characterization of ­ω-Limit Sets on Dynamical Systems

Some Remarks on Chain Prolongations in Dynamical Systems

P- Omega Limit Set in Random Dynamical Systems

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A Topological Characterization of ω-Limit Sets on Dynamical Systems

A Topological Characterization of ω-Limit Sets on Dynamical Systems