scholarly journals Integrability and generalized center problem of resonant singular point

2015 ◽  
Vol 40 ◽  
pp. 13-16 ◽  
Author(s):  
Qi Zhang ◽  
Yirong Liu
Keyword(s):  
Singular Point ◽  
Center Problem ◽  
Generalized Center

scholarly journals The generalized center problem of degenerate resonant singular point

2009 ◽  
Vol 133 (2) ◽  
pp. 198-204 ◽  
Author(s):  
Qi Zhang ◽  
Gui Weihua ◽  
Yirong Liu
Keyword(s):  
Singular Point ◽  
Center Problem ◽  
Generalized Center

The Complexity of Generalized Center Problem

2015 ◽  
Vol 14 (1) ◽  
pp. 11-23 ◽  
Author(s):  
Guangfeng Dong ◽  
Changjian Liu ◽  
Jiazhong Yang
Keyword(s):  
Center Problem ◽  
Generalized Center

ON THE CENTER PROBLEM FOR DEGENERATE SINGULAR POINTS OF PLANAR VECTOR FIELDS

2002 ◽  
Vol 12 (04) ◽  
pp. 687-707 ◽  
Author(s):  
VÍCTOR MAÑOSA
Keyword(s):  
Singular Point ◽  
Stability Problem ◽  
Vector Fields ◽  
Blow Up ◽  
Singular Points ◽  
Center Problem ◽  
Focal Value ◽  
The Status ◽  
Planar Vector ◽  
The Stability

The center problem for degenerate singular points of planar systems (the degenerate-center problem) is a poorly-understood problem in the qualitative theory of ordinary differential equations. It may be broken down into two problems: the monodromy problem, to decide if the singular point is of focus-center type, and the stability problem, to decide whether it is a focus or a center. We present an outline on the status of the center problem for degenerate singular points, explaining the main techniques and obstructions arising in the study of the problem. We also present some new results. Our new results are the characterization of a family of vector fields having a degenerate monodromic singular point at the origin, and the computation of the generalized first focal value for this family V1. This gives the solution of the stability problem in the monodromic case, except when V1 = 1. Our approach relies on the use of the blow-up technique and the study of the blow-up geometry of singular points. The knowledge of the blow-up geometry is used to generate a bifurcation of a limit cycle.

First order over determined system with singular point

2007 ◽  
Vol 18 (1) ◽  
pp. 65-80
Author(s):  
Adel Nasim Adib ◽  
Nusrat Rajabov
Keyword(s):  
Singular Point ◽  
First Order

scholarly journals A New Normal Form for Monodromic Nilpotent Singularities of Planar Vector Fields

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Antonio Algaba ◽  
Cristóbal García ◽  
Jaume Giné
Keyword(s):  
Normal Form ◽  
Vector Fields ◽  
New Technique ◽  
Center Problem ◽  
New Normal ◽  
Planar Vector Fields ◽  
Planar Vector ◽  
A New Technique

AbstractIn this work, we present a new technique for solving the center problem for nilpotent singularities which consists of determining a new normal form conveniently adapted to study the center problem for this singularity. In fact, it is a pre-normal form with respect to classical Bogdanov–Takens normal formal and it allows to approach the center problem more efficiently. The new normal form is applied to several examples.

Boundary Value Problems of Electroelasticity with Concentrated Singularities

1994 ◽  
Vol 1 (5) ◽  
pp. 459-467
Author(s):  
T. Buchukuri ◽  
D. Yanakidi
Keyword(s):  
Singular Point ◽  
Boundary Value Problems ◽  
Power Function ◽  
Boundary Value ◽  
Linearly Independent

Abstract We investigate the solutions of boundary value problems of linear electroelasticity, having growth as a power function in the neighbourhood of infinity or in the neighbourhood of an isolated singular point. The number of linearly independent solutions of this type is established for homogeneous boundary value problems.

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