Accession Number : AD0648173

Title :   ON A SINGULAR POINT OF BRIOT-BOUQUET TYPE OF A SYSTEM OF TWO ORDINARY NONLINEAR DIFFERENTIAL EQUATIONS.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Iwano,Masahiro

Report Date : JUN 1966

Pagination or Media Count : 142

Abstract : The singular points of Briot-Bouquet type of a system of ordinary nonlinear differential equations written in the form x dw/dx = h(x, w), h(0, 0) = 0, have been studied by diverse authors since C. H. Briot and J. C. Bouquet. Here, w is an n-dimensional column vector and h(x, w) is an n-dimensional column vector function holomorphic and bounded in (x, w) in a neighborhood of (0, 0). However, as far as I know, it has not yet been studied, except for n = 1, when the eigenvalues of the matrix h sub w (0, 0) are all zero. In this note the author studies the case for n = 2 under certain hypotheses. For convenience, the paper is divided into three parts. Part I is concerned with the construction of a formal transformation. In Part II formal solutions are constructed of diverse types depending on two arbitrary constants. Part III considers the analytical meaning of each of those formal solutions. (Author)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), TRANSFORMATIONS(MATHEMATICS), MATRICES(MATHEMATICS), FUNCTIONS(MATHEMATICS), POWER SERIES, CONVERGENCE, RATIONAL NUMBERS, COMPLEX VARIABLES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE