Co-Existence of Centers and Limit Cycles in Polynomial Systems

摘要

In this paper the authors consider polynomial systems on the plane withcoexisting centers and limit cycles. The authors prove that cubic systems which are symmetric with respect to a line which is not invariant, have either zero or exactly two limit cycles. The same result is proved for rationally reversible cubic systems. New configurations of co-existing centers and limit cycles in cubic systems are presented. Also an example of an integrable quartic system with a unique limit cycle and a center is given. As a bonus the authors construct a septic system with 57 limit cycles. (Copyright (c) 1996 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)