On the number invariant line of planar polynomial differential systems from above estimate

V. Tlyachev; A. Ushho; D. Ushho

doi:10.12737/4719

On the number invariant line of planar polynomial differential systems from above estimate

Actual directions of scientific researches of the XXI century theory and practice ◽

10.12737/4719 ◽

2014 ◽

Vol 2 (4) ◽

pp. 121-124

Author(s):

V. Tlyachev ◽

A. Ushho ◽

D. Ushho

Keyword(s):

Invariant Line ◽

Differential Systems ◽

Polynomial Differential Systems ◽

Planar Polynomial Differential Systems

Geometric Configurations of Singularities of Planar Polynomial Differential Systems

10.1007/978-3-030-50570-7 ◽

2021 ◽

Author(s):

Joan C. Artés ◽

Jaume Llibre ◽

Dana Schlomiuk ◽

Nicolae Vulpe

Keyword(s):

Differential Systems ◽

Polynomial Differential Systems ◽

Geometric Configurations ◽

Planar Polynomial Differential Systems

Polynomial first integrals for weight-homogeneous planar polynomial differential systems of weight degree 3

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.09.066 ◽

2007 ◽

Vol 331 (2) ◽

pp. 1284-1298 ◽

Cited By ~ 14

Author(s):

Laurent Cairó ◽

Jaume Llibre

Keyword(s):

First Integrals ◽

Differential Systems ◽

Polynomial Differential Systems ◽

Planar Polynomial Differential Systems

Integrability of Planar Polynomial Differential Systems through Linear Differential Equations

Rocky Mountain Journal of Mathematics ◽

10.1216/rmjm/1181069462 ◽

2006 ◽

Vol 36 (2) ◽

pp. 457-485 ◽

Cited By ~ 8

Author(s):

H. Giacomini ◽

J. Giné ◽

M. Grau

Keyword(s):

Differential Equations ◽

Linear Differential Equations ◽

Differential Systems ◽

Polynomial Differential Systems ◽

Linear Differential ◽

Planar Polynomial Differential Systems

Non-existence and uniqueness of limit cycles for planar polynomial differential systems with homogeneous nonlinearities

Journal of Differential Equations ◽

10.1016/j.jde.2018.05.019 ◽

2018 ◽

Vol 265 (9) ◽

pp. 3888-3913 ◽

Cited By ~ 7

Author(s):

Jianfeng Huang ◽

Haihua Liang ◽

Jaume Llibre

Keyword(s):

Limit Cycles ◽

Existence And Uniqueness ◽

Differential Systems ◽

Polynomial Differential Systems ◽

Uniqueness Of Limit Cycles ◽

Planar Polynomial Differential Systems

The geometry of the real planar polynomial differential systems having their orbits embedded in conics

Dynamical Systems ◽

10.1080/14689367.2011.588593 ◽

2011 ◽

Vol 26 (3) ◽

pp. 287-321 ◽

Cited By ~ 2

Author(s):

Jaume Llibre ◽

Adam Mahdi ◽

Joaquim Roé

Keyword(s):

Differential Systems ◽

The Real ◽

Polynomial Differential Systems ◽

Planar Polynomial Differential Systems

Polynomial first integrals for weight-homogeneous planar polynomial differential systems of weight degree~$4$

Rocky Mountain Journal of Mathematics ◽

10.1216/rmj-2016-46-5-1619 ◽

2016 ◽

Vol 46 (5) ◽

pp. 1619-1642

Author(s):

Jaume Llibre ◽

Claudia Valls

Keyword(s):

First Integrals ◽

Differential Systems ◽

Polynomial Differential Systems ◽

Planar Polynomial Differential Systems

Symmetry Axes of Planar Polynomial Differential Systems

Izvestiya of Saratov University New Series Series Mathematics Mechanics Informatics ◽

10.18500/1816-9791-2010-10-2-41-49 ◽

2010 ◽

Vol 10 (2) ◽

pp. 41-49

Author(s):

V.B. Tlyachev ◽

◽

A.D. Ushkho ◽

D.S. Ushkho ◽

◽

...

Keyword(s):

Differential Systems ◽

Polynomial Differential Systems ◽

Planar Polynomial Differential Systems

A New Method for Research on the Center-Focus Problem of Differential Systems

Abstract and Applied Analysis ◽

10.1155/2014/926538 ◽

2014 ◽

Vol 2014 ◽

pp. 1-5

Author(s):

Zhengxin Zhou

Keyword(s):

Critical Point ◽

Sufficient Conditions ◽

New Method ◽

Qualitative Behavior ◽

Differential Systems ◽

Polynomial Differential Systems ◽

Planar Polynomial Differential Systems

We will introduce Mironenko’s method to discuss the Poincaré center-focus problem, and compare the methods of Lyapunov and Mironenko. We apply the Mironenko method to discuss the qualitative behavior of solutions of some planar polynomial differential systems and derive the sufficient conditions for a critical point to be a center.

On Lie's symmetries for planar polynomial differential systems

Nonlinearity ◽

10.1088/0951-7715/14/4/313 ◽

2001 ◽

Vol 14 (4) ◽

pp. 863-880 ◽

Cited By ~ 11

Author(s):

J Chavarriga ◽

I A García ◽

J Giné

Keyword(s):

Differential Systems ◽

Polynomial Differential Systems ◽

Planar Polynomial Differential Systems

Reduction of integrable planar polynomial differential systems

Applied Mathematics Letters ◽

10.1016/j.aml.2012.02.047 ◽

2012 ◽

Vol 25 (11) ◽

pp. 1862-1865 ◽

Cited By ~ 7

Author(s):

Jaume Giné

Keyword(s):

Differential Systems ◽

Polynomial Differential Systems ◽

Planar Polynomial Differential Systems