the National Natural Science Foundation of China(Nos.21522203,21372111,and 21190034);State Key Laboratory of Applied Organic Chemistry for the financial support
The conjugated polycycles show excellent optical and electrical properties that are suitable for application in various organic electronics.While most of attentions have been paid to polycycles having planar π-conjug...
This work was supported by the National Natural Science Foundation of China(Grant No.10671020)
In this paper, we investigate the number and the distribution of the limit cycles bifurcated from a kind of degenerate planar polycycles through three singular points: a saddle-node P 0, a fine saddle P 1 with finite ...
This work was supported by the National Natural Science Foundation of China(Grant No.19901001).
This paper deals with the cyclicity of a kind of degenerate planar polycycles through a saddle-node P0 and two hyperbolic saddles P1 and P2, where the hyperbolicity ratio of the saddle P1 (which connects the saddle-no...
Project sponsored by National Science Foundation (19901001)
This paper deals with the cyclicity of a kind of degenerate planar polycycles through a saddle-node and two hyperbolic saddles, where the hyperbolicity ratio of the saddle (which connects the saddle-node with hp-conn...
The conjecture E(k)≤k is proved to be true if and only if k=1, 2, 3, where E(k) is the cyclicity of condimension k generic elementary polycycles. It is also proved that the cyclicity of any codimension 3 ensembles ex...
The cyclicity of four classes of codimension 3 plnnar polycycles and ensembles containing a saddle-node and two hyperbdic saddles is dealt with. The exnct cyclicity or cyclicity bound of them is obtained by finitely-s...
Project supported by the National Natural Science Foundation of China and the DEPF of China.
By means of finitely-smooth normal form theory and the method of infinitesimal analysis,it is proved that the cyclicity of a planar codimension 3 polycycle S(2) is three and the complete bifurcation diagram is provided.