Analytic Simplification of a System of Ordinary Differential Equations at an Irregular-Type Singularity.
Abstract
Let l sub n (u) = diag ((u sub 1), ..., (u sub n)) for given complex (u sub k). If Re (u sub k) = or > 0 (1 = or < k = or < n), then the (m+n)-system (x to the power (sigma +1)) y' = F(x,z)y,xz = (l sub n)z is simplified to (x to the power (sigma + 1))Y' = G(x,Z)Y, xZ' = (l sub n) (u)Z by a transformation T defined as y = Y + P(x,Z)Y,z = Z in a sector having property T with respect to ((lambda sub i)-(lambda sub j)(oxo)/(sigma(x to the power sigma))/i, j = 1, ..., s, (i not equal to j)), where (lambda sub i) (i = 1,2,...,s) are distinct eigenvalues of F(0,0) and G(x,Z) is in block-diagonal form agreeing with the Jordan canonical form of F(0,0). (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 11, 1971
- Accession Number
- AD0726413
Entities
People
- Po-fang Hsieh
Organizations
- United States Naval Research Laboratory