Walter Bergweiler Mathematisches Seminar Christian-Albrechts-Universität zu Kiel

Schriftenverzeichnis - List of publications

• (with Gerhard Jank & Lutz Volkmann) Wachstumsverhalten zusammengesetzter Funktionen, Results Math. 7 (1984), 35-53.
• (with Gerhard Jank & Lutz Volkmann) Über faktorisierbare Lösungen Riccatischer Differentialgleichungen, Results Math. 10 (1986), 40-53 [Special issue dedicated to H. Wittich].
• On the Nevanlinna characteristic of a composite function, Complex Var. Theory Appl. 10 (1988), 225-236.
• An inequality for real functions with applications to function theory, Bull. London Math. Soc. 21 (1989), 171-175.
• Order and lower order of composite meromorphic functions, Michigan Math. J. 36 (1989), 135-146.
• On the growth rate of composite meromorphic functions, Complex Var. Theory Appl. 14 (1990), 187-196.
• On the fix-points of composite functions, Pacific J. Math. 143 (1990), 1-8.
• Fix-points of meromorphic functions and iterated entire functions, J. Math. Anal. Appl. 151 (1990), 261-274.
• On meromorphic functions that share three values and on the exceptional set in Wiman-Valiron theory, Kodai Math. J. 13 (1990), 1-9.
• Proof of a conjecture of Gross concerning fix-points, Math. Z. 204 (1990), 381-390.
• On the number of fix-points of iterated entire functions, Arch. Math. (Basel) 55 (1990), 558-563.
• Maximum modulus, characteristic, and area on the sphere, Analysis 10 (1990), 163-176; ps, dvi, pdf. Erratum: Analysis 12 (1992), 67-69; ps, dvi, pdf.
• Periodic points of entire functions: proof of a conjecture of Baker, Complex Var. Theory Appl. 17 (1991), 57-72; ps, dvi, pdf.
• On the existence of fixpoints of composite meromorphic functions, Proc. Amer. Math. Soc. 114 (1992), 879-880; ps, dvi, pdf.
• Canonical products of infinite order, J. Reine Angew. Math. 430 (1992), 85-108; ps, dvi, pdf.
• (with C.-C. Yang) On the value distribution of composite meromorphic functions, Bull. London Math. Soc. 25 (1993), 357-361; ps, dvi, pdf.
• An example concerning factorization of rational functions, Exposition. Math. 11 (1993), 281-283; ps, dvi, pdf. Erratum: Exposition. Math. 34 (2016), 246-247; ps, dvi, pdf.
• (with Mako Haruta, Hartje Kriete, Hans-Günter Meier & Norbert Terglane) On the limit functions of iterates in wandering domains, Ann. Acad. Sci. Fenn. Ser. A I Math. 18 (1993), 369-375.
• Newton's method and a class of meromorphic functions without wandering domains, Ergodic Theory Dynam. Systems 13 (1993), 231-247; ps, dvi, pdf.
• Iteration of meromorphic functions, Bull. Amer. Math. Soc. (N. S.) 29 (1993), 151-188; ps, dvi, pdf; arxiv: math/9310226.
  Comments: ps, dvi, pdf.
• (with W. H. J. Fuchs) On the zeros of the second derivative of real entire functions, J. Anal. 1 (1993), 73-79; ps, dvi, pdf.
• (with Paul-Georg Becker) Transcendency of local conjugacies in complex dynamics and transcendency of their values, Manuscripta Math. 81 (1993), 369-377; ps, dvi, pdf.
• (with Fritz von Haeseler, Hartje Kriete, Hans-Günter Meier & Norbert Terglane) Newton's method for meromorphic functions, in “Complex Analysis and its Applications,” edited by C. C. Yang, G. C. Wen, K. Y. Li & Y. M. Chiang, Pitman Res. Notes Math. Ser. 305 (1994), 147-158.
• (with Ilpo Laine) Open problems in complex analysis, same proceedings, 352-358.
• A question of Gol'dberg concerning entire functions with prescribed zeros, J. Analyse Math. 63 (1994), 121-129; ps, dvi, pdf.
• (with Heinrich Bock) On the growth of meromorphic functions of infinite order, J. Analyse Math. 64 (1994), 327-336; ps, dvi, pdf.
• (with J. G. Clunie & J. K. Langley) Proof of a conjecture of Baker concerning the distribution of fixpoints, Bull. London Math. Soc. 27 (1995), 148-154; ps, dvi, pdf.
• On factorization of certain entire functions, J. Math. Anal. Appl. 193 (1995), 1003-1007; ps, dvi, pdf.
• (with Alexandre Eremenko) On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoamericana 11 (1995), 355-373; ps, dvi, pdf.
• (with Steffen Rohde) Omitted values in domains of normality, Proc. Amer. Math. Soc. 123 (1995), 1857-1858; ps, dvi, pdf.
• On the composition of transcendental entire and meromorphic functions, Proc. Amer. Math. Soc. 123 (1995), 2151-2153; ps, dvi, pdf.
• Invariant domains and singularities, Math. Proc. Cambridge Philos. Soc. 117 (1995), 525-532; ps, dvi, pdf; color graphics related to this paper are here.
• (with Paul-Georg Becker) Hypertranscendency of conjugacies in complex dynamics, Math. Ann. 301 (1995), 463-468; ps, dvi, pdf.
• Solution of a problem of Rubel concerning iteration and algebraic differential equations, Indiana Univ. Math. J. 44 (1995), 257-267; ps, dvi, pdf.
• On the zeros of certain homogeneous differential polynomials, Arch. Math. (Basel) 64 (1995), 199-202; ps, dvi, pdf.
• An introduction to complex dynamics, Textos Mat. Sér. B 6 (1995), 1-37; ps, dvi, pdf.
• On the Julia set of analytic self-maps of the punctured plane, Analysis 15 (1995), 251-256; ps, dvi, pdf.
• (with Norbert Terglane) Weakly repelling fixpoints and the connectivity of wandering domains, Trans. Amer. Math. Soc. 348 (1996), 1-12; ps, dvi, pdf.
• A quantitative version of Picard's theorem, Ark. Mat. 34 (1996), 225-229; ps, dvi, pdf.
• Non-real periodic points of entire functions, Canad. Math. Bull. 40 (1997), 271-275; ps, dvi, pdf.
• On the product of a meromorphic function and its derivative, Bull. Hong Kong Math. Soc. 1 (1997), 97-101; ps, dvi, pdf.
• Some remarks on Picard's theorem and Nevanlinna theory, Bull. Hong Kong Math. Soc. 1 (1997), 219-224 [Proceedings of the International Workshop on Value Distribution Theory and Its Applications (Hong Kong, 1996)]; ps, dvi, pdf.
• (with Yuefei Wang) On the dynamics of composite entire functions, Ark. Mat. 36 (1998), 31-39 ; ps, dvi, pdf.
• On a theorem of Gol'dberg concerning meromorphic solutions of algebraic differential equations, Complex Var. Theory Appl. 37 (1998), 93-96 [Special issue dedicated to A. A. Goldberg]; ps, dvi, pdf.
• (with Norbert Terglane) On the zeros of solutions of linear differential equations of the second order, J. London Math. Soc. 58 (1998), 311-330; ps, dvi, pdf; some color graphics related to this paper are here.
• A new proof of the Ahlfors five islands theorem, J. Analyse Math. 76 (1998), 337-347; ps, dvi, pdf; BMS 98-24.
• (with Katsuya Ishizaki & Niro Yanagihara) Meromorphic solutions of some functional equations, Methods Appl. Anal. 5 (1998), 248-258; ps, dvi, pdf. Correction: 6 (1999), 617, ps, dvi, pdf.
• (with Aimo Hinkkanen) On semiconjugation of entire functions, Math. Proc. Cambridge Philos. Soc. 126 (1999), 565-574; ps, dvi, pdf; BMS 97-21.
• The role of the Ahlfors five islands theorem in complex dynamics, Conform. Geom. Dyn. 4 (2000), 22-34; ps, dvi, pdf; BMS 99-16.
• (with Alexandre Eremenko) Entire functions of small growth whose Julia set coincides with the plane, Ergodic Theory Dynam. Systems 20 (2000), 1577-1582. ps, dvi, pdf; BMS 98-20. Correction: 21 (2001), 637. ps, dvi, pdf.
• Normale Familien (Vortrag auf dem Tag der Funktionentheorie, Berlin, 1999), Sitzungsberichte der Berliner Mathematischen Gesellschaft 1997-2000, pp. 485-487; ps, dvi, pdf.
• Some research problems in value distribution and complex dynamics (posed at the INTAS meeting in Lviv in 2000), unpublished; ps, dvi, pdf.
• Normality and exceptional values of derivatives, Proc. Amer. Math. Soc. 129 (2001), 121-129; ps, dvi, pdf; BMS 98-28.
• (with Detlef Bargmann) Composite meromorphic functions and growth of the spherical derivative, J. Math. Anal. Appl. 257 (2001), 274-281; ps, dvi, pdf.
• Covering properties of derivatives of meromorphic functions, Complex Var. Theory Appl. 43 (2001), 241-249 [Special issue dedicated to Chi-Tai Chuang]; ps, dvi, pdf; BMS 99-15.
• (with Detlef Bargmann) Periodic points and normal families, Proc. Amer. Math. Soc. 129 (2001), 2881-2888; ps, dvi, pdf; BMS 99-10.
• Singularities in Baker domains, Comput. Methods Funct. Theory 1 (2001), 41-49; ps, dvi, pdf.
• Rescaling principles in function theory, in “Proceedings of the International Conference on Analysis and its Applications,” edited by K. S. Lakshmi, R. Parvatham & H. M. Srivastava, Allied Publishers Ltd., New Delhi, 2001, 11-29; ps, dvi, pdf.
• (with Katsuya Ishizaki & Niro Yanagihara) Growth of meromorphic solutions of some functional equations, I, Aequationes Math. 63 (2002), 140-151; ps, dvi, pdf.
• On the number of critical points in parabolic basins, Ergodic Theory Dynam. Systems 22 (2002), 655-669; ps, dvi, pdf; BMS 00-16; some color graphics related to this paper are here.
• On proper analytic maps with one critical point, in “Value Distribution Theory and Complex Dynamics,” edited by W. Cherry & C.-C. Yang, Contemp. Math. 303, 1-6 (2002); ps, dvi, pdf; BMS 02-5.
• A question of Eremenko and Lyubich concerning completely invariant domains and indirect singularities, Proc. Amer. Math. Soc., 130 (2002), 3231-3236; ps, dvi, pdf; some color graphics related to this paper are here.
• (with Shunsuke Morosawa) Semihyperbolic entire functions, Nonlinearity 15 (2002), 1673-1684; ps, dvi, pdf.
• Ahlfors theory and complex dynamics: periodic points of entire functions, in “Complex dynamics and related fields,” RIMS Kokyuroku 1269 (2002), 1-11; ps, dvi, pdf; BMS 02-6.
• (with Xuecheng Pang) On the derivative of meromorphic functions with multiple zeros, J. Math. Anal. Appl. 278 (2003), 285-292; ps, dvi, pdf.
• (with Walter K. Hayman) Zeros of solutions of a functional equation, Comput. Methods Funct. Theory, 3 (2003), 55-78 [Special issue dedicated to D. Gaier]; ps, dvi, pdf.
• (with Alexandre Eremenko & J. K. Langley) Real entire functions of infinite order and a conjecture of Wiman, Geom. Funct. Anal. 13 (2003), 975-991; ps, dvi, pdf; arxiv: math/0207229,
• (with J. K. Langley) Nonvanishing derivatives and normal families, J. Analyse Math. 91 (2003), 353-367; ps, dvi, pdf.
• Periodic Fatou components and singularities of the inverse function, in “Topics in Analysis and its Applications,” edited by G. A. Barsegian & H. G. W. Begehr, NATO Science Series II: Mathematics, Physics and Chemistry, Vol. 147, Kluwer Acad. Publ., Dordrecht, 2004, 47-59; ps, dvi, pdf; BMS 02-9.
• Fixed points of composite meromorphic functions and normal families, Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), 653-660; ps, dvi, pdf; BMS 03-12.
• (with J. K. Langley) Multiplicities in Hayman's alternative, J. Australian Math. Soc. 78 (2005), 37-57; ps, dvi, pdf.
• Quasinormal families and periodic points, in “Complex Analysis and Dynamical Systems II: A Conference in Honor of Professor Lawrence Zalcman's Sixtieth Birthday, June 9-12, 2003, Nahariya, Israel,” edited by M. Agranovsky, L. Karp & D. Shoikhet, Contemp. Math. 382 (2005), 55-63; ps, dvi, pdf; BMS 04-2.
• (with Alexandre Eremenko & J. K. Langley) Zeros of differential polynomials in real meromorphic functions, Proc. Edinburgh Math. Soc. 48 (2005), 279-293; ps, dvi, pdf; arxiv: math/0407207, BMS 04-8.
• Bloch's principle, Comput. Methods Funct. Theory 6 (2006), 77-108; ps, dvi, pdf; arxiv: math/0511048, BMS 05-18.
• Fixed points of composite entire and quasiregular maps, Ann. Acad. Sci. Fenn. Math. 31 (2006), 523-540; ps, dvi, pdf; arxiv: math/0509635, BMS 05-25.
• (with Alexandre Eremenko) Proof of a conjecture of Pólya on the zeros of successive derivatives of real entire functions, Acta Math. 197 (2006), 125-146; ps, dvi, pdf; arxiv: math/0510502, BMS 05-26.
• (with J. K. Langley) Zeros of differences of meromorphic functions, Math. Proc. Cambridge Philos. Soc. 142 (2007), 133-147; ps, dvi, pdf; arxiv: math/0506441, BMS 05-19.
• (with David Drasin & James K. Langley) Baker domains for Newton's method, Ann. Inst. Fourier 57 (2007), 803-814; ps, dvi, pdf; arxiv: math/0601496, BMS 06-1.
• Permutable entire functions satisfying algebraic differential equations, Comput. Methods Funct. Theory 8 (2008), 101-106 [Special issue dedicated to W. K. Hayman]; ps, dvi, pdf; arxiv: math/0511117, BMS 05-28.
• (with Philip J. Rippon & Gwyneth M. Stallard) Dynamics of meromorphic functions with direct or logarithmic singularities, Proc. London Math. Soc. 97 (2008), 368-400; ps, pdf; arxiv: 0704.2712.
• (with Alexandre Eremenko) Meromorphic functions with two completely invariant domains, in “Transcendental Dynamics and Complex Analysis,” edited by P. J. Rippon & G. M. Stallard, Cambridge University Press, LMS Lecture Note Series 348 (2008), 74-89; ps, dvi, pdf; arxiv: math/0310495, BMS 03-11; some color graphics related to this paper are here.
• (with Alexandre Eremenko) Direct singularities and completely invariant domains of entire functions, Illinois J. Math. 52 (2008), 243-259; ps, dvi, pdf; arxiv: math/0608027, BMS 06-5. Note: Theorem 2 of this paper is incorrect. A counterexample is given by Theorem 1.2 in the paper On connected preimages of simply-connected domains under entire functions by Lasse Rempe-Gillen and Dave Sixsmith.
• (with Alastair Fletcher, Jim Langley & Janis Meyer) The escaping set of a quasiregular mapping, Proc. Amer. Math. Soc. 137 (2009), 641-651; pdf; arxiv: 0802.0119.
• (with Alexandre Eremenko) Meromorphic functions with linearly distributed values and Julia sets of rational function, Proc. Amer. Math. Soc. 137 (2009), 2329-2333 ; ps, dvi, pdf; arxiv: 0808.3800.
• (with Bogusława Karpińska & Gwyneth M. Stallard) The growth rate of an entire function and the Hausdorff dimension of its Julia set, J. London Math. Soc. 80 (2009), 680-698; ps, dvi, pdf; arxiv: 0807.2363.
• (with Bogusława Karpińska) On the Hausdorff dimension of the Julia set of a regularly growing entire function, Math. Proc. Cambridge Philos. Soc. 148 (2010), 531-551; ps, dvi, pdf; arxiv: 0909.3988.
• Normal families and fixed points of iterates, Sci. China Math. 53 (2010), 593-596 [Special issue dedicated to Yang Lo]; ps, dvi, pdf; arxiv: 1001.4511.
• (with Alexandre Eremenko) On the number of solutions of a transcendental equation arising in the theory of gravitational lensing, Comput. Methods Funct. Theory 10 (2010), 303-324; ps, pdf; arxiv: 0908.4595; some color graphics related to this paper are here.
• Newton's method and Baker domains, J. Difference Equ. Appl. 16 (2010), 427-432 [Special issue dedicated to R. L. Devaney]; ps, dvi, pdf; arxiv: 0710.1147.
• Karpińska's paradox in dimension 3, Duke Math. J. 154 (2010), 599-630; ps, dvi, pdf; arxiv: 0902.2686.
• Iteration of quasiregular mappings, Comput. Methods Funct. Theory 10 (2010), 455-481; ps, dvi, pdf;
• An entire function with simply and multiply connected wandering domains, Pure Appl. Math. Quarterly 7 (2011), 107-120 [Special issue dedicated to F. W. Gehring]; ps, dvi, pdf; arxiv: 0708.0941,
• The size of Wiman-Valiron disks, Complex Var. Elliptic Equ. 56 (2011), 13-33 [Special issue dedicated to C.-C. Yang]; ps, dvi, pdf; arxiv: 0901.2690.
• (with Alexandre Eremenko) Dynamics of a higher dimensional analog of the trigonometric functions, Ann. Acad. Sci. Fenn. Math. 36 (2011), 165-175; ps, dvi, pdf; arxiv: 1002.4159.
• (with Jian-Hua Zheng) On the uniform perfectness of the boundary of multiply connected wandering domains, J. Australian Math. Soc. 91 (2011), 289-311 ; ps, dvi, pdf; arxiv: 1011.5318.
• (with Magnus Aspenberg) Entire functions with Julia sets of positive measure, Math. Ann. 352 (2012), 27-54; ps, dvi, pdf; arxiv: 0904.1295.
• On the set where the iterates of an entire function are bounded, Proc. Amer. Math. Soc. 140 (2012), 847-853; ps, dvi, pdf; arxiv: 1012.1279.
• (with Alexandre Eremenko) On a property of the derivative of an entire function, Ann. Acad. Sci. Fenn. Math. 37 (2012), 301-307; ps, dvi, pdf; arxiv: 1107.4245.
• (with Jian-Hua Zheng) Some examples of Baker domains, Nonlinearity 25 (2012), 1033-1044; ps, dvi, pdf; arXiv:1110.1232.
• (with Janina Kotus) On the Hausdorff dimension of the escaping set of certain meromorphic functions, Trans. Amer. Math. Soc. 364 (2012), 5369-5394; ps, dvi, pdf; arxiv: 0901.3014.
• On the packing dimension of the Julia set and the escaping set of an entire function, Israel J. Math. 192 (2012), 449-472; ps, dvi, pdf; arxiv: 1101.3479.
• Fatou-Julia theory for non-uniformly quasiregular maps, Ergodic Theory Dynam. Systems 33 (2013), 1-23; ps, dvi, pdf; arxiv: 1102.1910.
• (with Alexandre Eremenko) Gol'dberg's constants, J. Analyse Math. 119 (2013), 365-402; ps, dvi, pdf; arxiv: 1111.2296.
• (with Jörn Peter) Escape rate and Hausdorff measure for entire functions, Math. Z. 274 (2013), 551-572; ps, dvi, pdf; arxiv: 1203.0190.
• (with Philip J. Rippon & Gwyneth M. Stallard) Multiply connected wandering domains of entire functions, Proc. London Math. Soc. 107 (2013), 1261-1301; ps, dvi, pdf; arxiv: 1109.1794.
• (with David Drasin & Alastair Fletcher) The fast escaping set for quasiregular mappings, Anal. Math. Phys. 4 (2014), 83-98 [Special issue dedicated to Lawrence Zalcman]; ps, dvi, pdf; arxiv: 1308.2860.
• The size of Julia sets of quasiregular maps, Ann. Univ. Buchar. Math. Ser. 5 (LXIII) (2014), 33-48 [Special issue dedicated to Cabiria Andreian Cazacu]; ps, dvi, pdf; arxiv: 1303.7243.
• (with Daniel A. Nicks) Foundations for an iteration theory of entire quasiregular maps, Israel J. Math. 201 (2014), 147-184; ps, dvi, pdf; arxiv: 1210.3972.
• (with Alastair Fletcher & Daniel A. Nicks) The Julia set and the fast escaping set of a quasiregular mapping, Comput. Methods Funct. Theory 14 (2014), 209-218 [Special issue dedicated to F. W. Gehring]; ps, dvi, pdf; arxiv: 1309.4601.
• An entire function with no fixed points and no invariant Baker domains, Proc. Amer. Math. Soc. 143 (2015), 197-202; ps, dvi, pdf; arxiv: 1210.5127.
• (with Alexandre Eremenko) Distribution of zeros of polynomials with positive coefficients, Ann. Acad. Sci. Fenn. Math. 40 (2015), 375-383; ps, dvi, pdf; arxiv: 1409.4640.
• (with Jun Wang) Hausdorff measure of hairs without endpoints in the exponential family, Math. Z. 281 (2015), 931-947; ps, dvi, pdf; arxiv: 1502.01961.
• (with Núria Fagella Rabionet and Lasse Rempe-Gillen), Hyperbolic entire functions with bounded Fatou components, Comment. Math. Helv. 90 (2015), 799-829; pdf; arxiv: 1404.0925; some color graphics related to this paper are here.
• (with Matthias Aschenbrenner) Julia's equation and differential transcendence, Illinois J. Math. 59 (2015), 277-294; ps, dvi, pdf; arxiv: 1307.6381.
• (with Alexandre Eremenko) Green's function and anti-holomorphic dynamics on a torus, Proc. Amer. Math. Soc. 144 (2016), 2911-2922; pdf; arxiv: 1507.01704; some color graphics related to this paper are here.
• (with Igor Chyzhykov) Lebesgue measure of escaping sets of entire functions of completely regular growth, J. London Math. Soc. 94 (2016), 639-661; ps, dvi, pdf; arxiv: 1510.03628.
• (with Alexandre Eremenko) On the Bank-Laine conjecture, J. Eur. Math. Soc. (JEMS) 19 (2017), 1899-1909; ps, dvi, pdf; arxiv: 1408.2400.
• On postsingularly finite exponential maps, Arnold Math. J. 3 (2017), 83-95 [Special issue dedicated to the XXV anniversary of the IMS]; ps, dvi, pdf; arxiv: 1511.08440.
• (with Dan Liu) On the multipliers of repelling periodic points of entire functions, Ann. Acad. Sci. Fenn. Math. 43 (2018), 279-291; ps, dvi, pdf; arxiv: 1701.06858.
• (with Xiao Yao and Jian-Hua Zheng) Lyapunov exponents and related concepts for entire functions, Math. Z. 288 (2018), 855-873; ps, dvi, pdf; arxiv: 1607.01271.
• (with Alexandre Eremenko and Aimo Hinkkanen) Entire functions with two radially distributed values, Math. Proc. Cambridge Philos. Soc. 165 (2018), 93-108 ; ps, dvi, pdf; arxiv: 1509.03283.
• (with Alexandre Eremenko) On the number of solutions of some transcendental equations, Anal. Math. Phys. 8 (2018), 185-196; ps, dvi, pdf; arxiv: 1702.06453.
• Lebesgue measure of Julia sets and escaping sets of certain entire functions, Fund. Math. 242 (2018), 281-301; pdf; arxiv: 1708.02819.

• (with Alexandre Eremenko) Quasiconformal surgery and linear differential equations, to appear in J. Analyse Math.; ps, pdf; arxiv: 1510.05731.
• (with Alexandre Eremenko) Radially distributed values and normal families, Int. Math. Res. Not. IMRN; ps, dvi, pdf; arxiv: 1709.05034.

There are also some comments (ps, dvi, pdf) on my survey article Iteration of meromorphic functions in the Bulletin of the American Mathematical Society.