Standard

Approximate and Real Trajectories for Generic Dynamical Systems. / Corless, Robert M.; Pilyugin, S. Yu.

в: Journal of Mathematical Analysis and Applications, Том 189, № 2, 15.01.1995, стр. 409-423.

Результаты исследований: Научные публикации в периодических изданияхстатьяРецензирование

Harvard

Corless, RM & Pilyugin, SY 1995, 'Approximate and Real Trajectories for Generic Dynamical Systems', Journal of Mathematical Analysis and Applications, Том. 189, № 2, стр. 409-423. https://doi.org/10.1006/jmaa.1995.1027

APA

Corless, R. M., & Pilyugin, S. Y. (1995). Approximate and Real Trajectories for Generic Dynamical Systems. Journal of Mathematical Analysis and Applications, 189(2), 409-423. https://doi.org/10.1006/jmaa.1995.1027

Vancouver

Corless RM, Pilyugin SY. Approximate and Real Trajectories for Generic Dynamical Systems. Journal of Mathematical Analysis and Applications. 1995 Янв. 15;189(2):409-423. https://doi.org/10.1006/jmaa.1995.1027

Author

Corless, Robert M. ; Pilyugin, S. Yu. / Approximate and Real Trajectories for Generic Dynamical Systems. в: Journal of Mathematical Analysis and Applications. 1995 ; Том 189, № 2. стр. 409-423.

BibTeX

@article{de2a8758d9734bc794761e820401ca1a,
title = "Approximate and Real Trajectories for Generic Dynamical Systems",
abstract = "In this paper we show that generic dynamical systems have a weak shadowing property, namely that for a generic dynamical system φ, in the space of discrete continuous dynamical systems on a compact manifold M with the usual C0 topology, given ε{lunate} > 0, there exists a δ > 0 such that δ-trajectories are ε{lunate}-close to real trajectories. There are no dimensional restrictions on this result. We also give some results on the {"}inverse{"} problem of tracing real trajectories by δ-trajectories. These problems are motivated by questions regarding the validity of numerical solutions of differential equations.",
author = "Corless, {Robert M.} and Pilyugin, {S. Yu}",
year = "1995",
month = jan,
day = "15",
doi = "10.1006/jmaa.1995.1027",
language = "English",
volume = "189",
pages = "409--423",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Elsevier",
number = "2",

}

RIS

TY - JOUR

T1 - Approximate and Real Trajectories for Generic Dynamical Systems

AU - Corless, Robert M.

AU - Pilyugin, S. Yu

PY - 1995/1/15

Y1 - 1995/1/15

N2 - In this paper we show that generic dynamical systems have a weak shadowing property, namely that for a generic dynamical system φ, in the space of discrete continuous dynamical systems on a compact manifold M with the usual C0 topology, given ε{lunate} > 0, there exists a δ > 0 such that δ-trajectories are ε{lunate}-close to real trajectories. There are no dimensional restrictions on this result. We also give some results on the "inverse" problem of tracing real trajectories by δ-trajectories. These problems are motivated by questions regarding the validity of numerical solutions of differential equations.

AB - In this paper we show that generic dynamical systems have a weak shadowing property, namely that for a generic dynamical system φ, in the space of discrete continuous dynamical systems on a compact manifold M with the usual C0 topology, given ε{lunate} > 0, there exists a δ > 0 such that δ-trajectories are ε{lunate}-close to real trajectories. There are no dimensional restrictions on this result. We also give some results on the "inverse" problem of tracing real trajectories by δ-trajectories. These problems are motivated by questions regarding the validity of numerical solutions of differential equations.

UR - http://www.scopus.com/inward/record.url?scp=0000539586&partnerID=8YFLogxK

U2 - 10.1006/jmaa.1995.1027

DO - 10.1006/jmaa.1995.1027

M3 - Article

AN - SCOPUS:0000539586

VL - 189

SP - 409

EP - 423

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -

ID: 92249740