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In [14] we showed that for transcendental entire functions f and g, there exist finitely many domains in an angular region, which lie in wandering component of f, wandering component of g and also in wandering component of f ° g and in wandering component of g ° f. Several other related results were discussed in that paper. In this paper we show the existence of such infinite components in angular region, using approximation theory.

Keywords

Wandering Domain, Approximation Theory, Angular Region.

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References

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Escaping Sets of Composition of Transcendental Entire Functions

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Authors

Anand P. Singh ¹, Garima Tomar ¹

Affiliations
1 Central University of Rajasthan, Department of Mathematics, Kishangarh, IN

Source

The Journal of the Indian Mathematical Society, Vol 88, No 3-4 (2021), Pagination: 373–386

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.

Keywords

Transcendental entire function, Escaping set, Julia set

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