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Limit shadowing property. / Eirola, Timo; Nevanlinna, Olavi; Pilyugin, Sergei Yu.

In: Numerical Functional Analysis and Optimization, Vol. 18, No. 1-2, 1997, p. 75-92.

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

Harvard

Eirola, T, Nevanlinna, O & Pilyugin, SY 1997, 'Limit shadowing property', Numerical Functional Analysis and Optimization, vol. 18, no. 1-2, pp. 75-92. https://doi.org/10.1080/01630569708816748

APA

Eirola, T., Nevanlinna, O., & Pilyugin, S. Y. (1997). Limit shadowing property. Numerical Functional Analysis and Optimization, 18(1-2), 75-92. https://doi.org/10.1080/01630569708816748

Vancouver

Eirola T, Nevanlinna O, Pilyugin SY. Limit shadowing property. Numerical Functional Analysis and Optimization. 1997;18(1-2):75-92. https://doi.org/10.1080/01630569708816748

Author

Eirola, Timo ; Nevanlinna, Olavi ; Pilyugin, Sergei Yu. / Limit shadowing property. In: Numerical Functional Analysis and Optimization. 1997 ; Vol. 18, No. 1-2. pp. 75-92.

BibTeX

@article{5dcc1770c4a0412c91e91531d002edae,
title = "Limit shadowing property",
abstract = "In this paper pseudoorbits of discrete dynamical systems are considered such that the one-step errors of the orbits tend to zero with increasing indices. First it is shown that close to hyperbolic sets such orbits are shadowed by true trajectories of the system with shadowing errors also tending to zero. Then the rates of convergence are studied via considering pseudoorbits such that the error sequences belong to certain (weighted) lp-spaces and showing that the corresponding shadowing errors are there, too. Under certain conditions on the weights we establish weighted shadowing near nonhyperbolic sets.",
keywords = "Hyperbolic sets, Sacker-Sell spectrum, Shadowing property",
author = "Timo Eirola and Olavi Nevanlinna and Pilyugin, {Sergei Yu}",
year = "1997",
doi = "10.1080/01630569708816748",
language = "English",
volume = "18",
pages = "75--92",
journal = "Numerical Functional Analysis and Optimization",
issn = "0163-0563",
publisher = "Taylor & Francis",
number = "1-2",

}

RIS

TY - JOUR

T1 - Limit shadowing property

AU - Eirola, Timo

AU - Nevanlinna, Olavi

AU - Pilyugin, Sergei Yu

PY - 1997

Y1 - 1997

N2 - In this paper pseudoorbits of discrete dynamical systems are considered such that the one-step errors of the orbits tend to zero with increasing indices. First it is shown that close to hyperbolic sets such orbits are shadowed by true trajectories of the system with shadowing errors also tending to zero. Then the rates of convergence are studied via considering pseudoorbits such that the error sequences belong to certain (weighted) lp-spaces and showing that the corresponding shadowing errors are there, too. Under certain conditions on the weights we establish weighted shadowing near nonhyperbolic sets.

AB - In this paper pseudoorbits of discrete dynamical systems are considered such that the one-step errors of the orbits tend to zero with increasing indices. First it is shown that close to hyperbolic sets such orbits are shadowed by true trajectories of the system with shadowing errors also tending to zero. Then the rates of convergence are studied via considering pseudoorbits such that the error sequences belong to certain (weighted) lp-spaces and showing that the corresponding shadowing errors are there, too. Under certain conditions on the weights we establish weighted shadowing near nonhyperbolic sets.

KW - Hyperbolic sets

KW - Sacker-Sell spectrum

KW - Shadowing property

UR - http://www.scopus.com/inward/record.url?scp=0030622932&partnerID=8YFLogxK

U2 - 10.1080/01630569708816748

DO - 10.1080/01630569708816748

M3 - Article

AN - SCOPUS:0030622932

VL - 18

SP - 75

EP - 92

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

SN - 0163-0563

IS - 1-2

ER -

ID: 92249270