The continuous, desingularized Newton method for meromorphic functions
- Cite this article as:
- Jongen, H.T., Jonker, P. & Twilt, F. Acta Appl Math (1988) 13: 81. doi:10.1007/BF00047503
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For any (nonconstant) meromorphic function, we present a real analytic dynamical system, which may be interpreted as an infinitesimal version of Newton's method for finding its zeros. A fairly complete description of the local and global features of the phase portrait of such a system is obtained (especially, if the function behaves not too bizarre at infinity). Moreover, in the case of rational functions, structural stability aspects are studied. For a generic class of rational functions, we give a complete graph-theoretical characterization, resp. classification, of these systems. Finally, we present some results on the asymptotic behaviour of meromorphic functions.