# On Levels of fast escaping sets and Spider's Web of transcendental entire functions

### New Zealand Journal of Mathematics

Vol. 49, (2019), Pages 1-9

Anand P. Singh

Department of Mathematics,

Central University of Rajasthan,

NH-8, Bandarsindri, Kishangarh-305817, Distt.-Ajmer,

Rajasthan,

India.

Garima Tomar

Department of Mathematics,

Central University of Rajasthan,

NH-8, Bandarsindri, Kishangarh-305817, Distt.-Ajmer,

Rajasthan,

India.

Abstract Let f be a transcendental entire function and let I(f) be the points which escape to infinity under iteration. Bergweiler and Hinkkanen introduced the fast escaping sets A(f) and subsequently, Rippon and Stallard introduced `Levels' of fast escaping sets $A_R^L(f)$. These sets under some restriction have the properties of "infinite spider's web" structure. Here we give some topological properties of the infinite spider's web and show some of the transcendental entire functions whose levels of the fast escaping sets have infinite spider's web structure.

Keywords Transcendental entire function, Escaping set, Spider's web, Fatou component.

Classification (MSC2000) 30D05, 37F10.