Invariant Surfaces of Periodic Systems with Conservative Cubic First Approximation

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Invariant Surfaces of Periodic Systems with Conservative Cubic First Approximation. / Basov, V.V.; Zhukov, A.S.

In: Vestnik St. Petersburg University: Mathematics, Vol. 52, No. 3, 01.07.2019, p. 244-258.

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

BibTeX

@article{b606b02682c74b3ca09ab292182391bb,

title = "Invariant Surfaces of Periodic Systems with Conservative Cubic First Approximation",

abstract = "Two classes of time-periodic systems of ordinary differential equations with a small parameter ε ≥ 0, those with “fast” and “slow” time, are studied. The corresponding conservative unperturbed systems (Formula presented.) have 1 to 3n singular points. The following results are obtained in explicit form: (1) conditions on perturbations independent of the parameter under which the initial systems have a certain number of invariant surfaces of dimension n + 1 homeomorphic to the torus for all sufficiently small parameter values; (2) formulas for these surfaces and their asymptotic expansions; (3) a description of families of systems with six invariant surfaces.",

keywords = "averaging, bifurcation, invariant surface, separatrix, EQUILIBRIUM, BIFURCATION",

author = "V.V. Basov and A.S. Zhukov",

year = "2019",

month = jul,

day = "1",

doi = "10.1134/S106345411903004X",

language = "English",

volume = "52",

pages = "244--258",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - Invariant Surfaces of Periodic Systems with Conservative Cubic First Approximation

AU - Basov, V.V.

AU - Zhukov, A.S.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - Two classes of time-periodic systems of ordinary differential equations with a small parameter ε ≥ 0, those with “fast” and “slow” time, are studied. The corresponding conservative unperturbed systems (Formula presented.) have 1 to 3n singular points. The following results are obtained in explicit form: (1) conditions on perturbations independent of the parameter under which the initial systems have a certain number of invariant surfaces of dimension n + 1 homeomorphic to the torus for all sufficiently small parameter values; (2) formulas for these surfaces and their asymptotic expansions; (3) a description of families of systems with six invariant surfaces.

AB - Two classes of time-periodic systems of ordinary differential equations with a small parameter ε ≥ 0, those with “fast” and “slow” time, are studied. The corresponding conservative unperturbed systems (Formula presented.) have 1 to 3n singular points. The following results are obtained in explicit form: (1) conditions on perturbations independent of the parameter under which the initial systems have a certain number of invariant surfaces of dimension n + 1 homeomorphic to the torus for all sufficiently small parameter values; (2) formulas for these surfaces and their asymptotic expansions; (3) a description of families of systems with six invariant surfaces.

KW - averaging

KW - bifurcation

KW - invariant surface

KW - separatrix

KW - EQUILIBRIUM

KW - BIFURCATION

UR - http://www.scopus.com/inward/record.url?scp=85071755817&partnerID=8YFLogxK

U2 - 10.1134/S106345411903004X

DO - 10.1134/S106345411903004X

M3 - Article

AN - SCOPUS:85071755817

VL - 52

SP - 244

EP - 258

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -

ID: 46240495