Complex Differential Equations [2, 6, 7, 14, 16, 19, 24,
27,
30, 31, 32, 34, 35, 39, 40, 42, 44, 45, 46]
In [2, 4]
Malmquist's
Theorem is extended to (and Yosida's Theorem is completed for) binomial
differential equations w'n=R(z,w). In [33, 35]
several conjectures due to Wiman, Perron and Wittich
concerning the distribution of zeros of solutions of linear
differential
equations and fundamental sets are proven. [40, 42,45, 46]
deal with Painleve's equations I, II, IV, and contain new proofs of
existence
of and sharp order estimates (stated by Boutroux) for the Painleve
transcendents
I, II, IV.
Nevanlinna Theory [1, 3, 5, 8, 9, 10, 11, 12, 13, 17, 18,
23, 26, 28, 29]
In [9]
the Tumura-Clunie
Theorem is extended from entire to meromorphic functions; [23,
29] contain a proof and extensions of Nevanlinna's Second
Main
Theorem for small functions. [28] contains the classification
of
those function triples (f,g,h) sharing four values; this also disproves
a conjecture (actually a ''theorem'') of H. Cartan.
Holomorphic Dynamics [31,
36, 37, 38, 41, 43, 47, 48, 49]
[31]
contains
a proof of Sullivan's (actually the Cremer-Fatou) classification of
periodic
stable domains. In [39] the quasiconformal conjugacy
classes
of rational functions whose Julia sets are Jordan curves or arcs are
determined.
Geometric Function Theory [20,
22, 25]
Book and Book Review
Rational Iteration. Complex Analytic Dynamical
Systems. de
Gruyter Studies in Mathematics 16
(1993). ZBL
0773.58010 MR94h: 30035
Painleve differential
equationation
in the complex plane, by V.I. Gromak, I. Laine and S. Shimomura,
de
Gruyter studies in Mathematics 28 (2002).
Bull. Amer. Math. Soc 41,
523-528 (2004)
Papers and Preprints
[1]
Zur Wertverteilung von Exponentialpolynomen.Manuscripta
Math.
6, 155-167 (1978). ZBL
0395.30023 MR80e:30012 OpenAccess
[2]
Bemerkung zu
einem Satz von Yosida. Complex Analysis,
Joensuu 1978. Lecture Notes in
Mathematics,
Vol. 747, 369-377. Springer 1979. ZBL
0 419.34004 MR81a:34007
[3]
(with E. Mues) Meromorphe
Funktionen, die mit ihrer Ableitung Werte teilen. Manuscripta Math.
29, 195-206 (1979). ZBL
0416.30028 MR80k:30025
[4]
Zur Theorie der binomischen Differentialgleichungen. Math.
Annalen 244, 263-274 (1979). ZBL 0422.34005 MR81a:34008
OpenAccess
[5]
Über die faktorisierbaren Lösungen gewöhnlicher
Differentialgleichungen. Math. Zeitschr. 170,
169-180
(1980). ZBL
0425.34006 MR83j:34010 OpenAccess
[6]
Ein Malmquistscher Satz für algebraische
Differentialgleichungen
erster Ordnung. Journal reine angew. Math. 316,
44-53 (1980). ZBL 0426.34011
MR81m:34007 OpenAccess
[7] Über
das Anwachsen der Lösungen homogener
algebraischer
Differentialgleichungen zweiter Ordnung. Manuscripta Math.
32, 303-308 (1980). ZBL
0444.34035 MR82d:34010 OpenAccess
[8]
Zur Wertverteilung der Quotienten von Exponentialpolynomen. Archiv
Math. 35, 461-470 (1980). ZBL
0461.30023 MR82e:30035
[9]
(with E. Mues
) The theorem of Tumura-Clunie for meromorphic functions. Journal
London Math. Soc. 23, 113-122
(1981). ZBL 0466.30025
[10]
Über die Nullstellen von Differentialpolynomen. Math.
Zeitschr. 176, 55-264 (1981). ZBL 0466.30026 MR82g:30053
OpenAccess
[11] On
factorization of the solutions of the Schwarzian
differential equation {w,z} = q(z). Funkc. Ekvac. 24,
307-315
(1981). ZBL
0485.30028 MR83e:30031
[12]
On the primeness of the Painlevé transcendents.
Factorization theory of meromorphic functions. Lect. Notes Pure
Appl. Math., p. 119-128, New York 1982. ZBL 0489.30021 MR84b:34005
[13]
(with C.
C. Yang) On common right factors of F and F(N).
Factorization
theory of meromorphic functions. Lect. Notes Pure Appl. Math., p.
129-138,
New York 1982. ZBL
0491.30016 MR83j:30030
[14] Zur
Wertverteilung der Lösungen der vierten
Painlevéschen Differentialgleichung. Math. Zeitschr.
181, 553-561 (1982). ZBL
0528.30019 MR84d: 34005 OpenAccess
[15]
On
the functional equation f(x)
= f(px) + f(qx+p). C.R.
Math. Rep. Acad. Sci. Canada 4, 367-371 (1982).
ZBL 0502.39006 MR84e: 39006
[16]
Über die eindeutigen Lösungen einer homogenen algebraischen
Differentialgleichung
zweiter Ordnung, Ann. Acad. Sci. Fenn. 7. 177-188
(1982) . ZBL
0565.34005 MR84f: 34009
[17] On
the order and lower order of entire functions with radially distributed
zeros.Proc Amer. Math. Soc. 87, 449-452 (1983). ZBL
0515.30017 MR84e: 30036
[18]
(with E. Mues)
Meromorphe
Funktionen, die mit ihrer Ableitung zwei Werte teilen. Results
Math. 6,
48-55 (1983).
ZBL 0571.30030 MR85d:30037
[19]
Über
eine Klasse von Painlevéschen
Differentialgleichungen. Archiv Math. 41,
261-266 (1983). ZBL
0601.34005 MR84k: 34015
[20]
Locally univalent functions in the unit disk.
Ann. Acad. Sci. Fenn. 8, 325-332 (1983). ZBL
0575.30015 MR85i: 30038
[21]
(with P.
Volkmann) Funktionalgleichungen
für
konstante Funktionen. Aequat. Math 27, 87-96 (1984). ZBL 0544.39005 MR86e: 39007
OpenAccess
[22] Homeomorphic
extension of univalent functions. Complex
Variables 6, 1-9 (1986). ZBL
0609.30001 MR87m: 30038
[23] Eine
Verallgemeinerung des zweiten Nevanlinnaschen Hauptsatzes.
Journal reine angew. Math 368, 134-141 (1986). ZBL 0598.30045 MR87i:30056
OpenAccess
[24]
Ein Malmquistscher Satz für algebraische Differentialgleichungen
zweiter Ordnung. Results Math. 10 ,
152-167
(1986). ZBL
0652.34007 MR88g: 30034
[25] De Branges´
proof of the Bieberbach conjecture. General
Inequalities 5, pp. 3-16. Birkhäuser 1987. ZBL 0624.30025 MR90g: 30018
[26]
On the zeros of (f(p)+ ap-1f(p-1)+
...+ a0 f)f. Analysis 7, 375-389 (1987). ZBL 0638.30033 MR89e: 34056
[27]
Meromorphe Lösungen der Differentialgleichung Q(z,w)d2w/dz2
= P(z,w)(dw/dz)2. Complex Variables 10, 31-41
(1988).
ZBL
0646.30030 MR89k:34009
[28]
A uniqueness theorem for three meromorphic functions. Ann.
Acad. Sci. Fenn. 13, 93-110 (1988). ZBL 0665.30033 MR90a: 30089
[29] On
the zeros of a certain Wronskian. Bull. London Math. Soc. 20,
525-531 (1988).
ZBL 0661.30025 MR89k: 30029
[30]
Exceptional values of the solutions of linear differential
equations. Math. Zeitschr. 201, 317-326 (1989). ZBL 0692.34006 MR90i:30044
[31]
Algebraische
Differentialgleichungen erster und zweiter
Ordnung. (In: Complex Methods on Partial Differential
Equations.
Akademie-Verlag Berlin 1989, pp. 187-192). ZBL 0692.30023
[32] Meromorphic
solutions of second order algebraic differential
equations. Complex Variables (Special Issue dedicated to A. Edrei
and
W. Fuchs) 13, 75-83 (1989). ZBL 0692.30022 MR91k:
34005
[33] On
Sullivan's
classification of periodic stable domains. Complex Variables 14,
211-214 (1990).
ZBL 0708.30027 MR91d:
58211
[34]
Linear differential equations with exceptional fundamental
sets. Analysis 11, 119-128 (1991). ZBL 0744.34014 MR94m: 30081 pdf
[35] Linear
differential equations with exceptional fundamental
sets, II. Proc. Amer. Math. Soc. 117, 355-358
(1993). ZBL
0770.30027 MR93d:34006
pdf
[36] The
formula of Riemann-Hurwitz and iteration of rational functions. Complex
Variables 22, 203-206 (1993). ZBL
0805.30030 MR94m: 30081 pdf
[37]
(with W. Schmidt) The polynomials
associated with a Julia set. Bull. London Math. Soc. 27,
239-241
(1995). ZBL
0826.30020 pdf
[38]
(with A.
Baesch) Exceptional solutions of n-th order periodic
linear differential equations. Complex Variables 34,
7-17 (1997). ZBL
0913.34007 MR98g: 34011 pdf
[39] Jordan
and Julia. Math. Annalen 307,
531-541
(1997). pdf ZBL
0879.30015 MR98d: 30028 Comments
on Jordan and Julia pdf
[40]
On Painlevé's equations I, II and IV, Journal d'Analyse
Math. 82,
363-377 (2000). ZBL
0989.34073 MR2002d: 34157 pdf
[41]
Sub-hyperbolic rational maps and algebraic differential
equations, Complex Variables 43, 451-456
(2001). ZBL 1022.30022 MR2002b: 30029 pdf
[42] Value
distribution of the Painlevé transcendents, Israel
Journal of Math. 128, 29-52 (2002). ZBL 1016.34091 MR2003c: 34152 pdf
[43]
Zalcman
functions and rational dynamics, New Zealand
J. Math 32, 1-14 (2003). ZBL 1045.30016
MR2004e: 30053 pdf 
[44] On Airy
solutions of Painlevé's second equation, Comput. Methods & Function
Theory 3,
117-126
(2003). ZBL
1069.34134 MR2005f: 34262
pdf
[45] Boutroux's method vs.
Re-scaling. Lower
estimates for the
orders of growth of the second and fourth 
Painleve
transcendents, Portugaliae Math. 61, 369-374 (2004). ZBL 1080.34088 MR2005j:34121
pdf
[46] Global
properties of the Painlevé transcendents. New results
and
open questions.
Ann.
Acad. Sci. Fenn. 30, 71-98 (2005). ZBL 1081.34088 MR2006c: 34177
pdf 
[47] On the dynamics of the McMullen family R(z)=z^m+lambda/z^l,
Conformal Geometry and Dynamics (ECGD)
10,
159-183 (
2006).
pdf
[48] Sierpinski curve Julia sets of rational
functions Comput. Methods & Function Theory 6,
317-327
(2006) pdf
[49] Sierpinski
and non-Sierpinski curve Julia sets in families of rational maps,
Journal London Math.
Soc. 78, 290-304 (2008)
pdf Dynamical
Planes
Norbert
Steinmetz