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Relative Superior Julia Sets for Complex Carotid-Kundalini Function

by Priti Dimri, Ashish Negi, Udai Bhan Trivedi
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 47 - Number 2
Year of Publication: 2012
Authors: Priti Dimri, Ashish Negi, Udai Bhan Trivedi
10.5120/7161-8794

Priti Dimri, Ashish Negi, Udai Bhan Trivedi . Relative Superior Julia Sets for Complex Carotid-Kundalini Function. International Journal of Computer Applications. 47, 2 ( June 2012), 22-30. DOI=10.5120/7161-8794

@article{ 10.5120/7161-8794,
author = { Priti Dimri, Ashish Negi, Udai Bhan Trivedi },
title = { Relative Superior Julia Sets for Complex Carotid-Kundalini Function },
journal = { International Journal of Computer Applications },
issue_date = { June 2012 },
volume = { 47 },
number = { 2 },
month = { June },
year = { 2012 },
issn = { 0975-8887 },
pages = { 22-30 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume47/number2/7161-8794/ },
doi = { 10.5120/7161-8794 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:40:52.481932+05:30
%A Priti Dimri
%A Ashish Negi
%A Udai Bhan Trivedi
%T Relative Superior Julia Sets for Complex Carotid-Kundalini Function
%J International Journal of Computer Applications
%@ 0975-8887
%V 47
%N 2
%P 22-30
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Carotid Kundalini function broadly known as C-K function was introduced by Gordon R. J. Cooper. It is given by the function where z,c andN are complex constants. Cooper presented interesting Julia sets by taking c=(0,0). Rani and Negi introduced a new process for generation of the C-K function and obtained interesting variants of Julia set generated by Cooper an some exciting figures for parameter , for values of c other than (0, 0). In this paper we apply a different iteration process for generation of the Julia set for C-K function and will call them relative superiorC-K Julia sets. Further, different properties like trajectories and fixed point arealso discussed in the paper. We also obtain some exciting figures for the C-K function for values of c other than (0, 0).

References
  1. Cooper, G. R. J. : Julia sets for complex Carotid-Kundalinifunction, Computers and Graphics 25(2001),153-158.
  2. Cooper, G. R. J. : Chaotic behavior in the Carotid – Kundalini map function, Computer Graphics 2000;24,165-70.
  3. Devaney, R. L. : Chaos, Fractals and dynamics, Computer experiments in mathematics, Menlo Park, Addison – Wessley (1992).
  4. Devaney, R. L. : The fractal Geometry of the Mandelbrot set , 2. How to count and how to add . Symposium in honor of Benoit Mandelbrot (Curaco 1995), Fractal 1995;3(4),629-40[MR1410283(99d:58095)].
  5. Devaney, R. L. and Krych M. : "Dynamics of exp(z)", Ergodic Theory Dynam. Systems4 (1984), 35–52.
  6. Devaney, R. L. and Tangerman F. : " Dynamics of entire functions near the essential singularity", Ergodic Theory and Dynamical Systems 6 4 (1986) 489–503.
  7. Devaney, R. L. and Tangerman F. : "Dynamics of entire functions near the essential Singularity", Ergodic Theory Dynam. Systems 6 (1986), 489–503.
  8. Peitgen, H. O. ; Jurgens, H. ; Saupe, D. : Chaos and Fractals, New frontiers of science, New York Springer,1992 984pp.
  9. Eremenko A. : "Iteration of entire functions", Dynamical Systems and Ergodic theory Banach Center Publ. 23, Polish Sc. Pub. , Warsaw 1989, 339-345.
  10. Pierre Fatou, " Sur Iteration des functions transcend dantesentires " Acta Math 47(1926),337-378
  11. Rani, M. ; Kumar, V. : Superior Julia set, J Korea Soc Math Edu Series D: Res Math Edu 2004; 8(4), 261-277.
  12. Rani M. : Iterative Procedures in Fractal and Chaos, Ph. D. Thesis, Department of Computer Science, Gurukul Kangri Vishwavidhayalaya, Hardwar,2002.
  13. Julia, G. : Sur 1' iteration des functions rationnelles, J Math Pure Appl. , 1918; 8, 47-245.
  14. Rottenfußer G. , Schleicher D. : Escaping Points of the Cosine Family, arXiv: math/0403012 (March 2004)
  15. McMullen C. : "Area and Hausdorff dimension of Julia sets of entire functions", Transactions of the American Mathematical Society 300 1 (1987), 329–342.
  16. Ishikawa S. : Fixed points by a new iteration method", Proc. Amer. Math. Soc. 44 (1974), 147-150.
  17. Rani, Negi A. : Newjulia sets for complex c-k function,
  18. ChauhanS. Y ,RanaR. andNegiA. : "New Julia Sets of Ishikawa Iterates", International Journal of Computer Applications 7(13):34–42, October 2010. Published By Foundation of Computer Science. ISBN: 978-93-80746-97-5
  19. Rana R. ,Yashwant S Chauhan and Negi A. :. "Non Linear Dynamics of Ishikawa Iteration", International Journal of Computer Applications 7(13):43–49, October 2010. Published By Foundation of Computer Science. ISBN: 978-93-80746-97-5.
  20. Chauhan S. Y. ; Rana, R. ; Negi, A. ; New Tricorn & Multicorns of ishikawa Iterates, International Journal of Computer Applications(0975-8887), Vol 7, No. 13, October 2010.
  21. Rana R. ,Chauhan, S. Y. andNegi, A. ; Inverse Complex Function Dynamics of Ishikawa Iterates , International Journal of Computer Applications(0975-8887), Vol 9, No. 1, November 2010.
  22. Chauhan S. Y. , Rana, R. and Negi, A. ; Complex Dynamics of Ishikawa Iterates for Non integer Values, International Journal of Computer Applications(0975-8887), Vol 9, No. 2, November 2010.
  23. Peitgen H. and RichterP. H. , The Beauty of Fractals, Springer-Verlag, Berlin,1986.
  24. Henon M. , Commun. Math. Phys. Phys. 50, 69-77 (1976)
  25. Negi A. : Generation of Fractals and applications, Ph. D. Thesis, Department of Computer Science, Gurukul Kangri Vishwavidhayalaya, Hardwar,2005
Index Terms

Computer Science
Information Sciences

Keywords

Carotid Kundalini Function Ishikawa Iteration Relative Superior C-k Julia Set