A Combined Study of New Escape Time Fractal for Sine and Inverse Tangent Functions

Complex graphics of dynamical system have been a subject of intense research nowadays. The fractal geometry is the base of these beautiful graphical images. Many researchers and authors have worked to study the complex nature of the two most popular sets in fractal geometry, the Julia set and the Mandelbrot set, and proposed their work in various forms using existing tools and techniques. The generation of fractals and study of the dynamics of transcendental function is one of the emerging and interesting fields of research nowadays. Recently, Ashish Negi, Rajeshri Rana and Yashwant S. Chauhan are among those researchers who have contributed a lot in the area of Fractal Geometry applications. In this paper we review the recently done work on sine and inverse tangent functions.

[1]  G. Julia.  Mémoire sur l'itération des fonctions rationnelles , 1918 .

[2]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[3]  Robert L. Devaney,et al.  Dynamics of exp (z) , 1984, Ergodic Theory and Dynamical Systems.

[4]  Walter Bergweiler,et al.  Iteration of entire functions , 2014 .

[5]  S. Ishikawa.  Fixed points by a new iteration method , 1974 .

[6]  Ashish Negi,et al.  Non Linear Dynamics of Ishikawa Iteration , 2010 .

[7]  Ashish Negi,et al.  Ishikawa Iterates for Logarithmic Function , 2011 .

[8]  Dierk Schleicher,et al.  Escaping Points of Exponential Maps , 2003 .

[9]  A. Klebanoff.  π IN THE MANDELBROT SET , 2001 .

[10]  Walter Bergweiler,et al.  Dynamics of a higher dimensional analog of the trigonometric functions , 2010 .

[11]  Ashish Negi,et al.  A Study of New Fractals Complex Dynamics for Inverse and Logarithmic Functions , 2012 .

[12]  Ashish Negi,et al.  Complex and Inverse Complex Dynamics of Fractals using Ishikawa Iteration , 2012 .

[13]  Yashwant S Chauhan,et al.  Escape Time Fractals of Inverse Tangent Function , 2013 .

[14]  Ashish Negi,et al.  GENERATION OF NEW FRACTALS FOR SINE FUNCTION , 2011 .

[15]  Ashish Negi,et al.  New Julia Sets of Ishikawa Iterates , 2010 .

[16]  Robert L. Devaney,et al.  Dynamics of entire functions near the essential singularity , 1986, Ergodic Theory and Dynamical Systems.

[17]  M. Bernhard.  Introduction to Chaotic Dynamical Systems , 1992 .

[18]  Walter Bergweiler,et al.  Iteration of meromorphic functions , 1993, math/9310226.

[19]  Ashish Negi,et al.  A Relative Superior Julia Set and Relative Superior Tricorn and Multicorns of Fractals , 2012 .