For any second order autonomous differential system with a polynomial of degree n on its right-hand side, what the maximum order of fineness of its weak focal point, weak saddle point in real domain and weak critical ...For any second order autonomous differential system with a polynomial of degree n on its right-hand side, what the maximum order of fineness of its weak focal point, weak saddle point in real domain and weak critical singular point in complex domain is (M(n)=?)? This problem relates to Hilbert’s 16th problem closely. Inequality M(3)≥7 have展开更多
In some recent work concerning the number of limit cycles of the planar polynomial differential system, by using the different methods and examples, N. G. Lloyd et al., D. M. Wang, and LIU Yi-rong have successively sh...In some recent work concerning the number of limit cycles of the planar polynomial differential system, by using the different methods and examples, N. G. Lloyd et al., D. M. Wang, and LIU Yi-rong have successively shown that there exist at least six limit cycles bifurcated from the origin in the planar cubic differential system （E<sub>3</sub>）. Namely, the value of cyclicity of multiple Hopf bifurcation （in the sense of Bautin） satisfies M（3）≥6.展开更多
文摘For any second order autonomous differential system with a polynomial of degree n on its right-hand side, what the maximum order of fineness of its weak focal point, weak saddle point in real domain and weak critical singular point in complex domain is (M(n)=?)? This problem relates to Hilbert’s 16th problem closely. Inequality M(3)≥7 have
基金Project supported by the National Natural Science Foundation of China.
文摘In some recent work concerning the number of limit cycles of the planar polynomial differential system, by using the different methods and examples, N. G. Lloyd et al., D. M. Wang, and LIU Yi-rong have successively shown that there exist at least six limit cycles bifurcated from the origin in the planar cubic differential system （E<sub>3</sub>）. Namely, the value of cyclicity of multiple Hopf bifurcation （in the sense of Bautin） satisfies M（3）≥6.
