Center conditions for a simple class of quintic systems

نویسنده

  • Evgenii P. Volokitin
چکیده

We obtained center conditions for a O-symmetric system of degree 5 for which the origin is a uniformly isochronous singular point. Classification: Primary 34C05; Secondary 34C25

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Ten Limit Cycles in a Quintic Lyapunov System

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small ...

متن کامل

A quintic polynomial differential system with eleven limit cycles at the infinity

In this article, a recursion formula for computing the singular point quantities of the infinity in a class of quintic polynomial systems is given. The first eleven singular point quantities are computed with the computer algebra system Mathematica. The conditions for the infinity to be a center are derived as well. Finally, a system that allows the appearance of eleven limit cycles in a small ...

متن کامل

Bi-center problem for some classes of Z2-equivariant systems

We investigate the simultaneous existence of two centers (bi-center) for two families of planar Z2-equivariant differential systems. First we present necessary and sufficient conditions for the existence of an isochronous bi-center for a planar Z2-equivariant cubic system having two centers at the points (−1, 0) and (1, 0), completing the study done by Liu and Li (2011). Next, we give condition...

متن کامل

Local bifurcation of limit cycles and center problem for a class of quintic nilpotent systems

* Correspondence: [email protected] School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, Henan, P. R. China Full list of author information is available at the end of the article Abstract For a class of fifth degree nilpotent system, the shortened expressions of the first eight quasi-Lyapunov constants are presented. It is shown that the orig...

متن کامل

Center of Planar Quintic Quasi–homogeneous Polynomial Differential Systems

In this paper we first characterize all quasi–homogeneous but non–homogeneous planar polynomial differential systems of degree five, and then among which we classify all the ones having a center at the origin. Finally we present the topological phase portrait of the systems having a center at the origin.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002