Iteration of entire functions

These notes contain the results discussed in the lectures at the CIMPA school in Kathmandu in November 2014. They contain only some of the proofs, but some references to the literature where proofs can be found are given.

[1]  P. Fatou,et al.  Sur l'itération des fonctions transcendantes Entières , 1926 .

[2]  J. Clunie Analytic Functions , 1962, Nature.

[3]  W. Bergweiler Invariant domains and singularities , 1995, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  L. Keen Dynamics of holomorphic self-maps of ℂ* , 1988 .

[5]  J. Milnor Dynamics in one complex variable , 2000 .

[6]  I. N. Baker Wandering Domains in the Iteration of Entire Functions , 1984 .

[7]  Alan F. Beardon,et al.  Iteration of Rational Functions , 1991 .

[8]  Alexandre Eremenko,et al.  Dynamical properties of some classes of entire functions , 1992 .

[9]  Walter Bergweiler,et al.  Iteration of meromorphic functions , 1993, math/9310226.

[10]  Alexandre Eremenko,et al.  On the iteration of entire functions , 1989 .

[11]  Area of Julia sets of holomorphic self-maps onC* , 1993 .

[12]  A. F. Beardon,et al.  The hyperbolic metric and geometric function theory , 2006 .

[13]  James F. Annett Vieweg, Braunschweig/Wiesbaden 1999 , 1999 .

[14]  I. Baker,et al.  Infinite limits in the iteration of entire functions , 1988, Ergodic Theory and Dynamical Systems.

[15]  I. N. Baker Multiply connected domains of normality in iteration theory , 1963 .

[16]  P. Rippon,et al.  On questions of Fatou and Eremenko , 2004 .

[17]  David G. Sullivan,et al.  Solution of the Fatou - Julia problem on wandering domains , 1985 .

[18]  A. Hinkkanen,et al.  On semiconjugation of entire functions , 1999, Mathematical Proceedings of the Cambridge Philosophical Society.

[19]  I. N. Baker Some entire functions with multiply-connected wandering domains , 1985, Ergodic Theory and Dynamical Systems.

[20]  鈴木 麻美,et al.  「On the Iteration of Analytic Functions」(木村俊房先生の仕事から) , 1998 .

[21]  I. N. Baker An entire function which has wandering domains , 1976, Journal of the Australian Mathematical Society.

[22]  W. Bergweiler On the Julia set of analytic self-maps of the punctured plane , 1995 .

[23]  J. Kotus Iterated Holomorphic Maps On The Punctured Plane , 1987 .

[24]  Dynamic rays of bounded-type entire functions , 2011 .

[25]  I. Ostrovskiǐ,et al.  Value Distribution of Meromorphic Functions , 2008 .

[26]  L. Ahlfors Complex Analysis , 1979 .

[27]  M. Pollicott,et al.  Dynamical Systems and Ergodic Theory , 1998 .

[28]  L. Keen,et al.  A finiteness theorem for a dynamical class of entire functions , 1986, Ergodic Theory and Dynamical Systems.

[29]  Une démonstration directe de la densité des cycles répulsifs dans l’ensemble de Julia , 2000 .

[30]  W. K. Hayman,et al.  On the characteristic of functions meromorphic in the unit disk and of their integrals , 1964 .

[31]  I. N. Baker The domains of normality of an entire function , 1975 .

[32]  I. N. Baker Repulsive fixpoints of entire functions , 1968 .

[33]  Lawrence Zalcman,et al.  Normal families: New perspectives , 1998 .

[34]  Mitsuhiro Shishikura,et al.  Transcendental Dynamics and Complex Analysis: On multiply connected wandering domains of entire functions , 2008 .

[35]  Lawrence Zalcman,et al.  A Heuristic Principle in Complex Function Theory , 1975 .

[36]  Walter Bergweiler,et al.  On the singularities of the inverse to a meromorphic function of finite order , 1995 .

[37]  P. Domínguez DYNAMICS OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS , 1998 .