Computing centre conditions for certain cubic systems
Necessary and sufficient conditions are presented for the origin to be a centre for cubic systems of the form \(\dot x=y\), \(\dot y=-x+A_ 1x^ 2+xy+A_ 3y^ 2+A_ 4x^ 3+A_ 5x^ 2y+A_ 6xy^ 2+A_ 7y^ 3\). The orbits are emphasized as the level curves of some functions. Extensive use of the computer algebra system REDUCE is involved. These conditions characterize the persistent centres (i.e. centres that are not destroyed by all perturbations within the given class of systems). The authors conjecture that there are no nonpersistent centres for the given cubic systems.
scientific article; zbMATH DE number 89623
scientific article