# Norbert Steinmetz

**Norbert Steinmetz** (* 1949 ) is a German mathematician.

After graduating from high school in Germersheim (1968), Steinmetz studied mathematics at the TH Karlsruhe with his diploma in 1975. He was a scientific assistant in Karlsruhe from 1975 and received his doctorate there in 1978 under Erwin Mues (properties of unique solutions of common differential equations in complexes) and habilitated in 1985 and was there afterwards a professor. From 1990 until his retirement in 2015 he was a professor at the University of Dortmund . From 1994 to 1996 he was Dean and from 1996 to 2000 a member of the Academic Senate.

He deals with differential equations in the complex, Nevanlinna theory , geometric function theory and holomorphic dynamics. He wrote a monograph on the dynamics of the iteration of rational functions in the complex.

In 1978 he succeeded in tightening the Malmquist and Yosida theorem. He gave new proofs for the existence of the Painlevé transcendent types I, II, IV. In the Nevanlinna theory he extended the theorem of Tumura and Clunie from whole to meromorphic functions with mues and he gave a new proof and an extension of the second Main theorem of the Nevanlin theory. In the complex dynamics he determined when Julia sets of rational functions are quasi-conformal Jordan curves (or arcs). In addition, he gave a proof of a theorem by Dennis Sullivan about the characterization of periodic stable domains during the iteration of rational functions (namely that these are either Fatou domains, i.e. in the region of attraction of a fixed point, or domains of rotation, i.e. Siegel disks or Arnold- Herman Rings).

## Fonts (selection)

- Rational iteration. Complex Analytic Dynamical Systems, De Gruyter Studies in Mathematics 16, De Gruyter 1993
- with E. Mues: Meromorphic functions that share values with their derivative, Manuscripta Mathematica, Volume 29, 1979, pp. 195-206
- About the factorisable solutions of ordinary differential equations, Mathematische Zeitschrift, Volume 170, 1980, pp 169-180
- A Malmquist's theorem for algebraic differential equations of the first order, Journal reine angew. Math., Volume 316, 1980, pp. 44-53
- with E. Mues: The theorem of Tumura-Clunie for meromorphic functions, Journal of the London Mathematical Society, Volume 23, 1981, pp. 113-122
- A generalization of the second Nevanlinnaschen law, Journal for pure and applied mathematics, Volume 368, 1986, pp. 134-141
- A uniqueness theorem for three meromorphic functions, Ann. Acad. Sci. Fenn., Vol. 13, 1988, pp. 93-110
- On the zeros of a certain Wronskian, Bulletin London Math. Soc., Vol. 20, 1988, pp. 525-531
- First and second order algebraic differential equations, in: Complex Methods on Partial Differential Equations, Akademie-Verlag Berlin 1989, pp. 187–192
- On Sullivan's classification of periodic stable domains. Complex Variables, Vol. 14, 1990, pp. 211-214
- Jordan and Julia, Math. Annalen, Volume 307, 1997, pp. 531-541
- On Painlevé's equations I, II and IV, Journal d'Analyse Mathématique, Volume 82, 2000, pp. 363-377
- Value distribution of the Painlevé transcendents, Israel Journal of Math., Volume 128, 2002, pp. 29-52

## Web links

## Individual evidence

- ↑ Norbert Steinmetz in the Mathematics Genealogy Project (English)
- ↑ Steinmetz, On the theory of binomial differential equations, Mathematische Annalen, Volume 244, 1979, pp. 263-274
- ↑ Steinmetz, Remarks on Yosida's Theorem, in: Complex Analysis, Joensuu 1978, Lecture Notes in Mathematics, Vol. 747, Springer 1979, pp. 369–377
- ↑ He published the evidence when Sullivan's own evidence had not yet been published
- ^ Refutation of a sentence by Henri Cartan

personal data | |
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SURNAME | Steinmetz, Norbert |

BRIEF DESCRIPTION | German mathematician |

DATE OF BIRTH | 1949 |