THE GENERALIZED HOMOCLINIC BIFURCATION

[摘要] In this article, we study a family X(lambda) of vector fields having at lambda=0 a homoclinic loop with multiplicity n. We give conditions for the displacement function to have the same zeros as all those of P(x, alpha(lambda))=alpha0(lambda)+alpha1(lambda)x+ ... +alpha(n-1)(lambda)x(n-1)+x(n) in a positive neighborhood of x=0, where alpha(lambda) is continuous. These conditions determine the versality of the family X(lambda) in a neighborhood of the loop. To obtain the result, we use the concept of Chebychev systems. (C) 1994 Academic Press, Inc.

[发布日期] 1994-03-01