Residual Julia set for functions with the Ahlfors' Property

References

• W.Abikoff, Some remarks on Kleinian groups, Ann. Math. Stud.66 (1971), pp. 1–5.
   Google Scholar
• W.Abikoff, The residual limit sets of Kleinian groups, Acta Math.130 (1973), pp. 127–144.
   Web of Science ®Google Scholar
• L.Ahlfors, Zur theory der Uberlagerungsflachen, Acta Math.65 (1935), pp. 157–194.
   Google Scholar
• I.N.Baker, Fixpoints and iterates of entire functions, Math. Z.71 (1959), pp. 146–153.
   Google Scholar
• I.N.Baker, Repulsive fixpoints of entire functions, Math. Z.104 (1968), pp. 252–256.
   Web of Science ®Google Scholar
• I.N.Baker and P.Domínguez, Residual Julia sets, J. Anal.8 (2000), pp. 121–137.
   Google Scholar
• I.N.Baker and P.Domínguez, Some connectedness properties of Julia sets, Complex Var.241 (2000), pp. 371–389.
   Google Scholar
• I.N.Baker, P.Domínguez, and M.E.Herring, Dynamics of functions meromorphic outside a small set, Ergodic Theory Dyn. Syst.21 (2001), pp. 647–672.
   Web of Science ®Google Scholar
• I.N.Baker, J.Kotus, and Y.Lü, Iterates of meromorphic functions. II: Examples of wandering domains, J. Lond. Math. Soc.42 (1990), pp. 267–278.
   Web of Science ®Google Scholar
• I.N.Baker, J.Kotus, and Y.Lü, Iterates of meromorphic functions. I, Ergodic Theory Dyn. Syst.11 (1991), pp. 241–248.
   Web of Science ®Google Scholar
• I.N.Baker, J.Kotus, and Y.Lü, Iterates of meromorphic functions. III: Preperiodic domains, Ergodic Theory Dyn. Syst.11 (1991), pp. 603–618.
   Web of Science ®Google Scholar
• I.N.Baker, J.Kotus, and Y.Lü, Iterates of meromorphic functions. IV: Critically finite functions, Results Math.22 (1992), pp. 651–656.
   Google Scholar
• A.F.Beardon, The components of a Julia set, Ann. Acad. Sci. Fenn. Ser. A.I. Math.16 (1991), pp. 173–177.
   Google Scholar
• W.Bergweiler, Iteration of meromorphic functions, Bull. Amer. Math. Soc. (N.S.)29 (1993), pp. 151–188.
   Web of Science ®Google Scholar
• W.Bergweiler, The role of the Ahlfors five islands theorem in complex dynamics, Conform. Geom. Dyn.4 (2000), pp. 22–34.
   Google Scholar
• A.Bolsch, Repulsive periodic points of meromorphic function, Complex Var. Theory Appl.31 (1996), pp. 75–79.
   Google Scholar
• A. Bolsch, Iteration of meromorphic functions with countably many singularities, dissertation, Technical Universität, Berlin, 1997.
   Google Scholar
• A.Bolsch, Periodic Fatou components of meromorphic functions, Bull. Lond. Math. Soc.31 (1999), pp. 543–555.
   Web of Science ®Google Scholar
• P.Domínguez, Connectedness properties of the Julia sets of transcendental entire functions, Complex Var. Theory Appl.32 (1997), pp. 199–215.
   Google Scholar
• P.Domínguez, Dynamics of transcendental meromorphic functions, Ann. Acad. Sci. Fenn. Ser. A.I. Math.23 (1998), pp. 225–250.
   Google Scholar
• P.Domínguez, Residual Julia set for meromorphic functions with countably many essential singularities, J. Differ. Equ. Appl.16(5–6) (2010), pp. 519–522.
   Web of Science ®Google Scholar
• P.Domínguez and N.Fagella, Residual Julia sets of rational and transcendental functions, in Transcendental Dynamics and Complex Analysis, LMS Lectures Note Series, Vol. 348, Cambridge University Press, UK, 2008, pp. 138–164.
   Google Scholar
• P.Domínguez and G.Sienra, Doubly connected wandering domains for meromorphic functions, Complex Var. Elliptic Equ.55(4) (2010), pp. 407–416.
   Web of Science ®Google Scholar
• A.L. Epstein, Towers of finite type complex analytic maps, Ph.D. thesis, City University of New York, 1993.
   Google Scholar
• A.L. Epstein, Dynamics of finite type complex analytic maps. I: Global structure theory, Manuscript.
   Google Scholar
• P.Fatou, Sur l' itération des fonctions transcendentes entierès, Acta Math.47 (1926), pp. 337–370.
   Google Scholar
• M.E. Herring, An extension of the Julia–Fatou theory of iteration, Ph.D. thesis, Imperial College, London, 1994.
   Google Scholar
• C.McMullen, Automorphisms of rational maps, in Holomorphic Functions and Modulii I, MSRI Publications, Vol. 10, Springer Verlag, New York, 1988.
   Google Scholar
• S.Morosawa, On the Residual Julia sets of rational functions, Ergodic Theory Dyn. Syst.17 (1997), pp. 205–210.
   Web of Science ®Google Scholar
• S.Morosawa, Y.Nishimura, M.Taniguchi, and T.Ueda, Holomorphic Dynamics, Cambridge University Press, UK, 2000.
   Google Scholar
• M.H.A.Newman, Elements of the Topology of Plane Set of Points, Cambridge University Press, UK, 1954.
   Google Scholar
• J.W.Osborne, The structure of spider's web fast escaping sets, Bull. Lond. Math. Soc.44(3) (2012), pp. 503–519.
   Web of Science ®Google Scholar
• J.W.Osborne, Spiders' webs and locally connected Julia sets of transcendental entire functions, Ergodic Theory Dyn. Syst.33(4) (2013), pp. 1146–1161.
   Web of Science ®Google Scholar
• R. Oudkerk, Iteration of Ahlfors and Picard functions which overflow their domain, Manuscript.
   Google Scholar
• J.Y.Qiao, The Julia set of the function, Chin. Sci. Bull.39(7) (1994), pp. 529–533.
   Web of Science ®Google Scholar
• J.Y.Qiao, The buried points on the Julia sets of rational and entire functions, Sci. China Ser. A.38 (1995), pp. 1409–1419.
   Google Scholar
• J.Y.Qiao, Topological complexity of Julia sets, Sci. China Ser. A.40 (1997), pp. 1158–1165.
   Google Scholar
• L.Rempe, Hyperbolic dimension and radial Julia sets of transcendental functions, Proc. Amer. Math. Soc.137(4) (2009), pp. 1411–1420.
   Web of Science ®Google Scholar
• L.Rempe and P.J.Rippon, Exotic Baker and wandering domains for Ahlfors islands maps, J. d'Anal. Math.117 (2012), pp. 297–319.
   Web of Science ®Google Scholar
• G.M.Stallard, Meromorphic functions whose Julia sets contain a free Jordan arc, Ann. Acad. Sci. Fenn. Ser. A.I. Math.18 (1993), pp. 273–298.
   Google Scholar
• D.Sullivan, Quasiconformal homeomorphisms and dynamics. I: Solutions of the Fatou–Julia problem on wandering domains, Ann. Math.122(3) (1985), pp. 401–418.
   Web of Science ®Google Scholar
• J.H.Zheng, T.W.Ng, and Y.Y.Choi, Residual Julia sets of meromorphic functions, Math. Proc. Camb. Philos. Soc.141(1) (2006), pp. 113–126.
   Web of Science ®Google Scholar