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Ishikawa Iterates for Logarithmic Function

by Rajeshri Rana, Yashwant S Chauhan, Ashish Negi
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 15 - Number 5
Year of Publication: 2011
Authors: Rajeshri Rana, Yashwant S Chauhan, Ashish Negi
10.5120/1941-2593

Rajeshri Rana, Yashwant S Chauhan, Ashish Negi . Ishikawa Iterates for Logarithmic Function. International Journal of Computer Applications. 15, 5 ( February 2011), 47-56. DOI=10.5120/1941-2593

@article{ 10.5120/1941-2593,
author = { Rajeshri Rana, Yashwant S Chauhan, Ashish Negi },
title = { Ishikawa Iterates for Logarithmic Function },
journal = { International Journal of Computer Applications },
issue_date = { February 2011 },
volume = { 15 },
number = { 5 },
month = { February },
year = { 2011 },
issn = { 0975-8887 },
pages = { 47-56 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume15/number5/1941-2593/ },
doi = { 10.5120/1941-2593 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:03:24.097958+05:30
%A Rajeshri Rana
%A Yashwant S Chauhan
%A Ashish Negi
%T Ishikawa Iterates for Logarithmic Function
%J International Journal of Computer Applications
%@ 0975-8887
%V 15
%N 5
%P 47-56
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper the dynamics of the complex logarithmic function is investigated using the Ishikawa iterates. The fractal images generated from the generalized transformation function z→log(zn+c), n ≥ 2 are analyzed

References
  1. B. Branner, “The Mandelbrot Set”, Proceedings of Symposia in Applied Mathematics39 (1989), 75-105.
  2. Robert L. Devaney, “A First Course in Chaotic Dynamical Systems: Theory and Experiment”, Addison-Wesley, 1992. MR1202237.
  3. R. L. Devaney, “The fractal geometry of the Mandelbrot set. 2. How to count and how to add. Symposium in Honor of Benoit Mandelbrot”, Fractals 3 (1995), no. 4, 629-640. MR1410283(99d:58095)
  4. R. L. Devaney, “The fractal geometry of the Mandelbrot set:I, Period of Bulbs”, In Fractals, Graphics and mathematics education, MAA Notes,58(2002), 61-68.
  5. R. L. Devaney and M. Krych, “Dynamics of Exp(z)”, Ergodic Theory and Dynamical Systems 4(1984), 35- 52.
  6. R. L. Devaney, D.M. Look and D. Umnisky, “The Escape Trichotomy for Singular perturbed Rational maps”, Indiana Univ. Mathematics Journal 54(2005), 267-285.
  7. R. L. Devaney and X. Jarque, “Indecomposable Continua in Exponential Dynamics”, Conformal Geom. Dynamical 6(2002), 1-12.
  8. U. G. Gujar and V. C. Bhavsar, Fractals from in the Complex c-Plane, Computers and Graphics 15, 3 (1991), 441-449.
  9. U. G. Gujar, V. C. Bhavsar and N. Vangala, Fractals from in the Complex z-Plane, Computers and Graphics 16, 1 (1992), 45-49.
  10. E. F. Glynn, The Evolution of the Gingerbread Man, Computers and Graphics 15,4 (1991), 579-582.
  11. S. Ishikawa, “Fixed points by a new iteration method”, Proc. Amer. Math. Soc.44 (1974), 147-150.
  12. G. Julia, “Sur 1’ iteration des functions rationnelles”, J Math Pure Appli. 8 (1918), 737-747
  13. B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, New York, 1983.
  14. Eike Lau and Dierk Schleicher, “Symmetries of fractals revisited.”, Math. Intelligencer (18)(1)(1996), 45-51. MR1381579 Zbl 0847.30018.
  15. J. Milnor, “Dynamics in one complex variable; Introductory lectures”, Vieweg (1999).
  16. Shizuo Nakane, and Dierk Schleicher, “Non-local connectivity of the tricorn and multicorns”, Dynamical systems and chaos (1) (Hachioji, 1994), 200-203, World Sci. Publ., River Edge, NJ, 1995. MR1479931.
  17. Shizuo Nakane, and Dierk Schleicher, “On multicorns and unicorns: I. Antiholomorphic dynamics. hyperbolic components and real cubic polynomials”, Internat. J. Bifur. Chaos Appl. Sci. Engrg, (13)(10)(2003), 2825-2844. MR2020986.
  18. Ashish Negi, “Generation of Fractals and Applications”, Thesis, Gurukul Kangri Vishwvidyalaya, (2005).
  19. M.O.Osilike, “Stability results for Ishikawa fixed point iteration procedure”, Indian Journal of Pure and Appl. Math., 26(1995), 937-945.
  20. A. G. D. Philip: “Wrapped midgets in the Mandelbrot set”, Computer and Graphics 18 (1994), no. 2, 239-248.
  21. H. Peitgen and P. H. Richter, “The Beauty of Fractals”, Springer-Verlag, Berlin, 1986.
  22. B. E. Rhoades, “Fixed point iterations for certain nonlinear mappings”, J. Math. Anal. 183 (1994), 118-120.
  23. Rajeshri Rana, Yashwant S Chauhan and Ashish Negi. Article: 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
  24. M.Romera, G. Pastor and F. Montoya, “On the cusp and the tip of a midget in the Mandelbrot set antenna”, Phys. Lett. A 221 (1996), no 3-4, 158-162. MR1409563 (97d: 58073).
  25. K. W. Shirriff, “An investigation of fractals generated by ”, Computers and Graphics 13, 4(1993), 603-607.
  26. R. Winters, “Bifurcations in families of Antiholomorphic and biquadratic maps”, Thesis, Boston Univ. (1990).
  27. Yashwant S Chauhan, Rajeshri Rana and Ashish Negi. Article: 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
Index Terms

Computer Science
Information Sciences

Keywords

Complex dynamics Relative Superior Mandelbrot Set Relative Superior Julia set Ishikawa Iteration and Midgets

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