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Conservation and bifurcation of an invariant torus of a vector field. / Bibikov, Yu N.

In: Mathematical Notes, Vol. 61, No. 1-2, 01.01.1997, p. 29-37.

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

Harvard

Bibikov, YN 1997, 'Conservation and bifurcation of an invariant torus of a vector field', Mathematical Notes, vol. 61, no. 1-2, pp. 29-37. https://doi.org/10.1007/BF02355005

APA

Bibikov, Y. N. (1997). Conservation and bifurcation of an invariant torus of a vector field. Mathematical Notes, 61(1-2), 29-37. https://doi.org/10.1007/BF02355005

Vancouver

Bibikov YN. Conservation and bifurcation of an invariant torus of a vector field. Mathematical Notes. 1997 Jan 1;61(1-2):29-37. https://doi.org/10.1007/BF02355005

Author

Bibikov, Yu N. / Conservation and bifurcation of an invariant torus of a vector field. In: Mathematical Notes. 1997 ; Vol. 61, No. 1-2. pp. 29-37.

BibTeX

@article{20138adc97b14f8190c48ae011bde2f1,
title = "Conservation and bifurcation of an invariant torus of a vector field",
abstract = "We consider small perturbations with respect to a small parameter ε ≥ 0 of a smooth vector field in ℝn+m possessing an invariant torus Tm. The flow on the torus Tm is assumed to be quasiperiodic with m basic frequencies satisfying certain conditions of Diophantine type; the matrix Ω of the variational equation with respect to the invariant torus is assumed to be constant. We investigate the existence problem for invariant tori of different dimensions for the case in which Ω is a nonsingular matrix that can have purely imaginary eigenvalues.",
keywords = "Bifurcation, Invariant tori, Noncritical matrices, Quasiperiodic motion",
author = "Bibikov, {Yu N.}",
year = "1997",
month = jan,
day = "1",
doi = "10.1007/BF02355005",
language = "English",
volume = "61",
pages = "29--37",
journal = "Mathematical Notes",
issn = "0001-4346",
publisher = "Pleiades Publishing",
number = "1-2",

}

RIS

TY - JOUR

T1 - Conservation and bifurcation of an invariant torus of a vector field

AU - Bibikov, Yu N.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - We consider small perturbations with respect to a small parameter ε ≥ 0 of a smooth vector field in ℝn+m possessing an invariant torus Tm. The flow on the torus Tm is assumed to be quasiperiodic with m basic frequencies satisfying certain conditions of Diophantine type; the matrix Ω of the variational equation with respect to the invariant torus is assumed to be constant. We investigate the existence problem for invariant tori of different dimensions for the case in which Ω is a nonsingular matrix that can have purely imaginary eigenvalues.

AB - We consider small perturbations with respect to a small parameter ε ≥ 0 of a smooth vector field in ℝn+m possessing an invariant torus Tm. The flow on the torus Tm is assumed to be quasiperiodic with m basic frequencies satisfying certain conditions of Diophantine type; the matrix Ω of the variational equation with respect to the invariant torus is assumed to be constant. We investigate the existence problem for invariant tori of different dimensions for the case in which Ω is a nonsingular matrix that can have purely imaginary eigenvalues.

KW - Bifurcation

KW - Invariant tori

KW - Noncritical matrices

KW - Quasiperiodic motion

UR - http://www.scopus.com/inward/record.url?scp=27544504312&partnerID=8YFLogxK

U2 - 10.1007/BF02355005

DO - 10.1007/BF02355005

M3 - Article

VL - 61

SP - 29

EP - 37

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 1-2

ER -

ID: 49227591