Center of planar quintic quasi--homogeneous polynomial differential systems
Copyright policy )Center of planar quintic quasi--homogeneous polynomial differential systems
The authors describe all planar polynomial systems of degree five which are quasi-homogeneous of type \((i,j)\), where \(i,j\) are coprime numbers satisfying \(6\geq i>j\geq 1\). There are 15 such systems, among them the only system with a (global) center is \[ \dot{x}=-3bxy^2-y^5,\;\dot{y}=by^3+x,\;\;b^2<\frac13. \] Moreover, this center has a strictly monote period function.
- Shanghai Jiao Tong University China (People's Republic of)
- Southern Polytechnic State University United States
Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems, quasi-homogeneous system, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, classification, Periodic orbits of vector fields and flows, Symmetries, invariants of ordinary differential equations, Periodic solutions to ordinary differential equations, quintic planar polynomial system, global center, monotone period function, Transformation and reduction of ordinary differential equations and systems, normal forms
Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems, quasi-homogeneous system, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, classification, Periodic orbits of vector fields and flows, Symmetries, invariants of ordinary differential equations, Periodic solutions to ordinary differential equations, quintic planar polynomial system, global center, monotone period function, Transformation and reduction of ordinary differential equations and systems, normal forms
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