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Stability of Periodic Points of Diffeomorphisms of Multidimensional Space. / Vasil'eva, E.V.

In: Vestnik St. Petersburg University: Mathematics, Vol. 51, No. 3, 15.09.2018, p. 204-214.

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

Harvard

Vasil'eva, EV 2018, 'Stability of Periodic Points of Diffeomorphisms of Multidimensional Space', Vestnik St. Petersburg University: Mathematics, vol. 51, no. 3, pp. 204-214. https://doi.org/DOI: 10.3103/S1063454118030111

APA

Vasil'eva, E. V. (2018). Stability of Periodic Points of Diffeomorphisms of Multidimensional Space. Vestnik St. Petersburg University: Mathematics, 51(3), 204-214. https://doi.org/DOI: 10.3103/S1063454118030111

Vancouver

Vasil'eva EV. Stability of Periodic Points of Diffeomorphisms of Multidimensional Space. Vestnik St. Petersburg University: Mathematics. 2018 Sep 15;51(3):204-214. https://doi.org/DOI: 10.3103/S1063454118030111

Author

Vasil'eva, E.V. / Stability of Periodic Points of Diffeomorphisms of Multidimensional Space. In: Vestnik St. Petersburg University: Mathematics. 2018 ; Vol. 51, No. 3. pp. 204-214.

BibTeX

@article{264c43e73beb40c29eb2a8868b073057,
title = "Stability of Periodic Points of Diffeomorphisms of Multidimensional Space",
abstract = "This paper continues previous works of the author, where diffeomorphisms are studied such that their Jacobi matrices at the origin have only real eigenvalues. In those previous works, we find conditions such that the neighborhood of a nontransversal homoclinic point of the studied diffeomorphism contains an infinite set of stable periodic points with characteristic exponents separated from zero. In the present paper, it is assumed that the Jacobi matrix of the original diffeomorphism at the origin has real eigenvalues and several pairs of complex conjugate eigenvalues. Under this assumption, we find conditions guaranteeing that a neighborhood of a nontransversal homoclinic point contains an infinite set of stable periodic points with characteristic exponents separated from zero.",
keywords = "Stability of Periodic Points, Diffeomorphisms, Multidimensional Space, multidimensional diffeomorphism, hyperbolic point, STABILITY, nontransversal homoclinic point",
author = "E.V. Vasil'eva",
note = "Vasil{\textquoteright}eva, E.V. Stability of Periodic Points of Diffeomorphisms of Multidimensional Space. Vestnik St.Petersb. Univ.Math. 51, 204–212 (2018). https://doi.org/10.3103/S1063454118030111",
year = "2018",
month = sep,
day = "15",
doi = "DOI: 10.3103/S1063454118030111",
language = "English",
volume = "51",
pages = "204--214",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - Stability of Periodic Points of Diffeomorphisms of Multidimensional Space

AU - Vasil'eva, E.V.

N1 - Vasil’eva, E.V. Stability of Periodic Points of Diffeomorphisms of Multidimensional Space. Vestnik St.Petersb. Univ.Math. 51, 204–212 (2018). https://doi.org/10.3103/S1063454118030111

PY - 2018/9/15

Y1 - 2018/9/15

N2 - This paper continues previous works of the author, where diffeomorphisms are studied such that their Jacobi matrices at the origin have only real eigenvalues. In those previous works, we find conditions such that the neighborhood of a nontransversal homoclinic point of the studied diffeomorphism contains an infinite set of stable periodic points with characteristic exponents separated from zero. In the present paper, it is assumed that the Jacobi matrix of the original diffeomorphism at the origin has real eigenvalues and several pairs of complex conjugate eigenvalues. Under this assumption, we find conditions guaranteeing that a neighborhood of a nontransversal homoclinic point contains an infinite set of stable periodic points with characteristic exponents separated from zero.

AB - This paper continues previous works of the author, where diffeomorphisms are studied such that their Jacobi matrices at the origin have only real eigenvalues. In those previous works, we find conditions such that the neighborhood of a nontransversal homoclinic point of the studied diffeomorphism contains an infinite set of stable periodic points with characteristic exponents separated from zero. In the present paper, it is assumed that the Jacobi matrix of the original diffeomorphism at the origin has real eigenvalues and several pairs of complex conjugate eigenvalues. Under this assumption, we find conditions guaranteeing that a neighborhood of a nontransversal homoclinic point contains an infinite set of stable periodic points with characteristic exponents separated from zero.

KW - Stability of Periodic Points

KW - Diffeomorphisms

KW - Multidimensional Space

KW - multidimensional diffeomorphism

KW - hyperbolic point

KW - STABILITY

KW - nontransversal homoclinic point

U2 - DOI: 10.3103/S1063454118030111

DO - DOI: 10.3103/S1063454118030111

M3 - Article

VL - 51

SP - 204

EP - 214

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -

ID: 38816154