Exploding Julia sets in the dynamics of $ f_{\lambda}(z)=\lambda J_{1}(iz)/iz

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Title:	Exploding Julia sets in the dynamics of $ f_{\lambda}(z)=\lambda J_{1}(iz)/iz
Authors:	Guru Prem Prasad, M Nayak, T Roy, A K
Keywords:	Complex Dynamics Julia Set Chaotic Set
Issue Date:	2006
Publisher:	Allied Publishers
Citation:	Proceedings of the Third National Conference on Non-linear Systems and Dynamics, (NCNSD-2006), Ramanujan Institute for Advanced Study in Mathematics, University of Madras, February 6-8, 2006, P 171-174
Abstract:	In the present paper, we study the dynamics of the one parameter family of entire functions ff¸(z) = ¸f(z) : f(z) = J1(iz)=iz for z 2 C and ¸ is a non-zero real numberg where J1(z) is the Bessel function of the first kind of order one. We have found a critical parameter ¸¤ ¼ 2:598 and show that the Julia set of f¸ is a nowhere dense subset of the complex plane C for 0 < j¸j · ¸¤ and is equal to extended complex plane bC = C[f1g for j¸j > ¸¤. This sudden change in the Julia sets is known as explosion in the Julia sets or chaotic burst in the dynamics.
Description:	Copyright for the paper belongs to Proceedings Publisher
URI:	http://hdl.handle.net/2080/649
Appears in Collections:	Conference Papers

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