Using Carleman linearization procedure, this paper investigates the problem of first integrals of polynomial autonomous systems and proposes a procedure to find the first integrals of polynomial family for the systems...Using Carleman linearization procedure, this paper investigates the problem of first integrals of polynomial autonomous systems and proposes a procedure to find the first integrals of polynomial family for the systems. A generalized eigenequation is obtained and then the problem is reduced to the solvability of the eigenequation. The result is a generalization of some known results.展开更多
基金This research is supported by the National Natural Science Foundation(G59837270,G1998020308, G69774008) National Key Project of China.
文摘Using Carleman linearization procedure, this paper investigates the problem of first integrals of polynomial autonomous systems and proposes a procedure to find the first integrals of polynomial family for the systems. A generalized eigenequation is obtained and then the problem is reduced to the solvability of the eigenequation. The result is a generalization of some known results.
