0000000000886655
AUTHOR
Chengzhi Li
showing 2 related works from this author
The cyclicity of the elliptic segment loops of the reversible quadratic Hamiltonian systems under quadratic perturbations
2004
Abstract Denote by Q H and Q R the Hamiltonian class and reversible class of quadratic integrable systems. There are several topological types for systems belong to Q H ∩ Q R . One of them is the case that the corresponding system has two heteroclinic loops, sharing one saddle-connection, which is a line segment, and the other part of the loops is an ellipse. In this paper we prove that the maximal number of limit cycles, which bifurcate from the loops with respect to quadratic perturbations in a conic neighborhood of the direction transversal to reversible systems (called in reversible direction), is two. We also give the corresponding bifurcation diagram.
Perturbations of symmetric elliptic Hamiltonians of degree four
2006
AbstractIn this paper four-parameter unfoldings Xλ of symmetric elliptic Hamiltonians of degree four are studied. We prove that in a compact region of the period annulus of X0 the displacement function of Xλ is sign equivalent to its principal part, which is given by a family induced by a Chebychev system; and we describe the bifurcation diagram of Xλ in a full neighborhood of the origin in the parameter space, where at most two limit cycles can exist for the corresponding systems.