Escaping Sets of Composition of Transcendental Entire Functions

Jump To References Section

Authors

  • ,IN
  • ,IN

DOI:

https://doi.org/10.18311/jims/2021/27840

Keywords:

Transcendental entire function, Escaping set, Julia set
30D05, 37F10

Abstract

If f and g are transcendental entire functions, then so are f o g and g o f. We discuss here the dynamics of various types of escaping sets and also non-escaping sets of composition of transcendental entire functions f o g and g o f and also its relations with regard to its factors f and g.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Published

2021-06-14

How to Cite

Singh, A. P., & Tomar, G. (2021). Escaping Sets of Composition of Transcendental Entire Functions. The Journal of the Indian Mathematical Society, 88(3-4), 373–386. https://doi.org/10.18311/jims/2021/27840
Received 2021-05-19
Accepted 2021-05-19
Published 2021-06-14

 

References

I. N. Baker, Zusammensetzungen ganzer Funktionen., Math. Z. (German), 69 (1958), 121-163.

I. N. Baker, Wandering domains in the iteration of entire functions, Proc. London Math. Soc., 49 (3)(1984), 563-576.

I. N. Baker and P. Dom nguez, Residual Julia sets, J. Analysis, 8 (2000), 121-137.

W. Bergweiler, Iteration of meromorphic functions, Bull. Amer. Math. Soc., 29 (1993), 151-188.

W. Bergweiler, On Julia set of analytic self maps of the punctured plane, Analysis, 15 (1995), 251-256.

W. Bergweiler and A. Hinkkanen, On semiconjugation of entire functions, Math. Proc. Camb. Phil. Soc., 126 (1999), 565-574.

W. Bergweiler and Y.Wang, On the dynamics of composite entire functions, Ark. Math., 36 (1998), 31-39.

W. Bergweiler, On the set where the iterates of an entire function are bounded, Proc. Amer. Math. Soc., 140 (2012), 847-853.

J. G. Clunie, The composition of entire and meromorphic functions, Mathematical Es- says Dedicated to A. J. Macintyre, Ed. Shankar H., Ohio Univ. Press, 1970, 75-92.

P. Dom nguez and N. Fagella, Residual Julia sets of rational and transcendental func- tions, Transcendental Dynamics and Complex Analysis, Cambridge University Press, 2008, 138-164.

A. E. Eremenko, On the iteration of entire functions, Dynamical systems and ergodic theory, Banach Center Publications 23, Polish Scienti c Publishers, Warsaw, 1989, 339-345.

J. W. Osborne, Connectedness properties of the set where the iterates of an entire function are bounded, Math. Proc. Cambridge Philos. Soc., 155 (2013), 391-410.

J. W. Osborne and D. J. Sixsmith, On the set where the iterates of transcendental entire functions are neither escaping nor bounded, Anna. Acad. Sci. Fenn. Math., 41 (2016), 561-578.

L. Rempe, On a question of Eremenko concerning escaping components of entire func- tions, Bull. London Math. Soc., 39 (2007), 661-666.

P. J. Rippon and G. M. Stallard, On sets where iterates of a meromorphic function zip towards infinity, Bull. London Math. Soc., 32 (2000), 528-536.

P. J. Rippon and G. M. Stallard, On questions of Fatou and Eremenko, Proc. Amer. Math. Soc., 133 (2005), 1119-1126.

P. J. Rippon and G. M. Stallard, Escaping points of entire functions of small growth, Math. Z., 261 (2009), 557-570.

P. J. Rippon and G. M. Stallard, Fast escaping points of entire functions, Proc. London Math. Soc., 105 (2012), 787-820.

P. J. Rippon and G. M. Stallard, Baker's conjecture and Eremenko's conjecture for functions with negative zeros, Journal d'Analyse Math., 120 (2013), 29-309.

G. Rottenfuer, J. Ruckert, L. Rempe and D. Schleicher, Dynamic rays of bounded-type entire functions, Ann. of Math., 173 (2011), 77-125.

A. P. Singh, On the dynamics of composition of entire functions, Math. Proc. Camb. Phi. Soc., 134 (2003), 129-138.

A. P. Singh and Y. Wang, Julia sets of Permutable holomorphic maps, Science in China Series A: Mathematics, 49 (11)(2006), 1715-1721.