Complete integrability and time-reversibility of some 3-dim systems

摘要

In this work we study complete integrability and time-reversibility of three dimensional polynomial systems with a singularity at the origin at which the linear part has a zero eigenvalue and a pair of eigenvalues that are the negatives of one another. An approach to finding systems within a given parametric family admitting two independent analytic local first integrals in a neighborhood of the origin is proposed and applied to a family of cubic systems. (C) 2015 Elsevier Ltd. All rights reserved.