An analytic classification of saddle resonant singular points of holomorphic vector fields in the complex plane

S. M. Voronin; A. A. Grintchy

doi:10.1007/bf02259621

An analytic classification of saddle resonant singular points of holomorphic vector fields in the complex plane

Journal of Dynamical and Control Systems ◽

10.1007/bf02259621 ◽

1996 ◽

Vol 2 (1) ◽

pp. 21-53 ◽

Cited By ~ 10

Author(s):

S. M. Voronin ◽

A. A. Grintchy

Keyword(s):

Complex Plane ◽

Vector Fields ◽

Singular Points ◽

Holomorphic Vector Fields ◽

Analytic Classification

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Thom’s problem for orbital analytic classification of degenerate singular points of holomorphic vector fields in the plane

Doklady Mathematics ◽

10.1134/s1064562410050200 ◽

2010 ◽

Vol 82 (2) ◽

pp. 759-761 ◽

Cited By ~ 1

Author(s):

S. M. Voronin ◽

L. Ortiz-Bobadilla ◽

E. Rosales-Gonzáles

Keyword(s):

Vector Fields ◽

Singular Points ◽

Holomorphic Vector Fields ◽

Analytic Classification

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Analytic Classification of Foliations Induced by Germs of Holomorphic Vector Fields in ( ℂ n , 0 ) $(\mathbb {C}^{n},0)$ with Non-isolated Singularities

Journal of Dynamical and Control Systems ◽

10.1007/s10883-019-09436-7 ◽

2019 ◽

Vol 25 (3) ◽

pp. 491-516

Author(s):

L. Ortiz-Bobadilla ◽

E. Rosales-González ◽

S. M. Voronin

Keyword(s):

Vector Fields ◽

Isolated Singularities ◽

Holomorphic Vector Fields ◽

Analytic Classification

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On the local classification of holomorphic vector fields

Lecture Notes in Mathematics - Geometric Dynamics ◽

10.1007/bfb0061412 ◽

1983 ◽

pp. 96-103 ◽

Cited By ~ 1

Author(s):

Marc Chaperon

Keyword(s):

Vector Fields ◽

Holomorphic Vector Fields ◽

Local Classification

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Analytic Classification of Fuchsian Singular Points

Mathematical Notes ◽

10.1023/b:matn.0000043462.06397.ab ◽

2004 ◽

Vol 76 (3/4) ◽

pp. 348-357 ◽

Cited By ~ 1

Author(s):

V. A. Kleptsyn ◽

B. A. Rabinovich

Keyword(s):

Singular Points ◽

Analytic Classification

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REMARKS ON THE ORBITAL ANALYTIC CLASSIFICATION OF GERMS OF VECTOR FIELDS

Mathematics of the USSR-Sbornik ◽

10.1070/sm1984v049n01abeh002700 ◽

1984 ◽

Vol 49 (1) ◽

pp. 111-124 ◽

Cited By ~ 5

Author(s):

P M Elizarov ◽

Yu S Il'yashenko

Keyword(s):

Vector Fields ◽

Analytic Classification

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On the singularity structure of Kahan discretizations of a class of quadratic vector fields

European Journal of Mathematics ◽

10.1007/s40879-021-00479-4 ◽

2021 ◽

Author(s):

René Zander

Keyword(s):

Elliptic Curves ◽

Vector Fields ◽

Singularity Structure ◽

Quadratic Vector Fields ◽

Parameter Values

AbstractWe discuss the singularity structure of Kahan discretizations of a class of quadratic vector fields and provide a classification of the parameter values such that the corresponding Kahan map is integrable, in particular, admits an invariant pencil of elliptic curves.

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Bifurcations of topological type at singular points of parametrized vector fields

Functional Analysis and Its Applications ◽

10.1007/bf01077527 ◽

1972 ◽

Vol 6 (2) ◽

pp. 169-170 ◽

Cited By ~ 20

Author(s):

A. N. Shoshitaishvili

Keyword(s):

Vector Fields ◽

Topological Type ◽

Singular Points

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Homoclinic orbits and Lie rotated vector fields

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171200010061 ◽

2000 ◽

Vol 24 (3) ◽

pp. 187-192

Author(s):

Jie Wang ◽

Chen Chen

Keyword(s):

Limit Cycles ◽

Homoclinic Orbit ◽

Vector Fields ◽

Homoclinic Orbits ◽

Singular Points ◽

Definition Of

Based on the definition of Lie rotated vector fields in the plane, this paper gives the property of homoclinic orbit as parameter is changed and the singular points are fixed on Lie rotated vector fields. It gives the conditions of yielding limit cycles as well.

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