ALGORITHM 596 A Program for a Locally Parameterized Continuation Process

Abstract

is an open, o n e d i m e n s i o n a l C L m a n i f o l d in R n. W e are i n t e r e s t ed in c o m p u t i n g the c o n n e c t e d c o m p o n e n t 8R (F, x °) of £R (F) wh ich c o n t a i n s x °. B y a f u n d a m e n t a l r esu l t of d i f ferent ia l geome t ry (see, e.g., [5]), 8R(F, x °) is d i f feomorphic e i t he r to a circle or to some in t e rva l ( connec ted subse t ) of R ~. F o r s impl i c i ty we call (~R (F, x 0) the so lu t ion curve of (1.2) t h r o u g h x °.