Sets of vector fields with various shadowing properties of pseudotrajectories

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Sets of vector fields with various shadowing properties of pseudotrajectories. / Pilyugin, S. Yu ; Tikhomirov, S. B.

In: Doklady Mathematics, Vol. 78, No. 2, 01.10.2008, p. 669-670.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{724a384aba824e47ae335c24a76c45d8,

title = "Sets of vector fields with various shadowing properties of pseudotrajectories",

abstract = "A study was conducted to analyze the sets of vector fields with various shadowing properties of pseudotrajectories. The main difference between the shadowing problem for flows and a similar problem for discrete dynamical systems generated by diffeomorphisms is related to the necessity of reparameterization of shadowing trajectories in the former case. The aim of the study is also to describe the structure of C1 interiors of sets of vector fields with various shadowing properties. A monotonically increasing homeomorphism h of the line R such as h(0) = 0 is called a reparameterization. The study analyzed that a field X has the Lipschitz shadowing property if there exist certain numbers with particular properties. The study also concludes that a field X has the orbital shadowing property if there exists a number with a particular property.",

author = "Pilyugin, {S. Yu} and Tikhomirov, {S. B.}",

year = "2008",

month = oct,

day = "1",

doi = "10.1134/S1064562408050062",

language = "English",

volume = "78",

pages = "669--670",

journal = "Doklady Mathematics",

issn = "1064-5624",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "2",

}

RIS

TY - JOUR

T1 - Sets of vector fields with various shadowing properties of pseudotrajectories

AU - Pilyugin, S. Yu

AU - Tikhomirov, S. B.

PY - 2008/10/1

Y1 - 2008/10/1

N2 - A study was conducted to analyze the sets of vector fields with various shadowing properties of pseudotrajectories. The main difference between the shadowing problem for flows and a similar problem for discrete dynamical systems generated by diffeomorphisms is related to the necessity of reparameterization of shadowing trajectories in the former case. The aim of the study is also to describe the structure of C1 interiors of sets of vector fields with various shadowing properties. A monotonically increasing homeomorphism h of the line R such as h(0) = 0 is called a reparameterization. The study analyzed that a field X has the Lipschitz shadowing property if there exist certain numbers with particular properties. The study also concludes that a field X has the orbital shadowing property if there exists a number with a particular property.

AB - A study was conducted to analyze the sets of vector fields with various shadowing properties of pseudotrajectories. The main difference between the shadowing problem for flows and a similar problem for discrete dynamical systems generated by diffeomorphisms is related to the necessity of reparameterization of shadowing trajectories in the former case. The aim of the study is also to describe the structure of C1 interiors of sets of vector fields with various shadowing properties. A monotonically increasing homeomorphism h of the line R such as h(0) = 0 is called a reparameterization. The study analyzed that a field X has the Lipschitz shadowing property if there exist certain numbers with particular properties. The study also concludes that a field X has the orbital shadowing property if there exists a number with a particular property.

UR - http://www.scopus.com/inward/record.url?scp=54349088502&partnerID=8YFLogxK

U2 - 10.1134/S1064562408050062

DO - 10.1134/S1064562408050062

M3 - Article

AN - SCOPUS:54349088502

VL - 78

SP - 669

EP - 670

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 2

ER -

ID: 43393237