Dynamics of Julia Sets for Complex Exponential Functions

Prasad, Bhagwati; Katiyar, Kuldip

doi:10.1007/978-3-642-28926-2_19

Cited by 6 publications

(4 citation statements)

References 12 publications

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“…Devaney (see, [6,[26][27][28]) described the topology and dynamics of the complex exponential family E λ (z) = λe z , λ > 0. Baker and Rippon [29] discussed the interesting geometry of Julia sets for different values of λ. Romera et al [30] studied the complex families e z 2 +λ and e z λ using the Picard iterative process, while Prasad et al [31] used the Ishikawa iterative scheme to prove the same results.…”

Section: Introductionmentioning

confidence: 93%

A Brief Study on Julia Sets in the Dynamics of Entire Transcendental Function Using Mann Iterative Scheme

Prajapati¹,

Rawat

Tomar

et al. 2022

Fractal Fract

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In this research, we look at the Julia set patterns that are linked to the entire transcendental function f(z)=aezn+bz+c, where a,b,c∈C and n≥2, using the Mann iterative scheme, and discuss their dynamical behavior. The sophisticated orbit structure of this function, whose Julia set encompasses the entire complex plane, is described using symbolic dynamics. We also present bifurcation diagrams of Julia sets generated using the proposed iteration and function, which altogether contain four parameters, and discuss the graphical analysis of bifurcation occurring in the family of this function.

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Section: Introductionmentioning

confidence: 93%

A Brief Study on Julia Sets in the Dynamics of Entire Transcendental Function Using Mann Iterative Scheme

Prajapati¹,

Rawat

Tomar

et al. 2022

Fractal Fract

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“…It is remarked that (3) with α n = 1 is the Picard iteration (2). Prasad and Katiyar [18], [19], [20], [21] and [22] studied the map (1) for different iterative schemes and interesting fractal patterns are generated in [19], [20] and [22] .…”

Section: Preliminariesmentioning

confidence: 99%

STABILITY AND LYAPUNOV EXPONENTS OF A $q$-DEFORMED MAP

Prasad¹,

Katiyar²

2015

Int. J. of Pure and Appl. Math.

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“…However, comparable approaches can be used to investigate the behavior of complex transcendental functions. Romera et al [15] employed the Picard iterative technique to study complex families, whereas Prasad et al [16] adopted the Ishikawa iterative scheme to obtain identical outcomes. Ref.…”

Section: Introductionmentioning

confidence: 99%

Mandelbrot and Julia Sets of Transcendental Functions Using Picard–Thakur Iteration

Bhoria,

Panwar,

Sajid

2023

Fractal Fract

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The majority of fractals’ dynamical behavior is determined by escape criteria, which utilize various iterative procedures. In the context of the Julia and Mandelbrot sets, the concept of “escape” is a fundamental principle used to determine whether a point in the complex plane belongs to the set or not. In this article, the fractals of higher importance, i.e., Julia sets and Mandelbrot sets, are visualized using the Picard–Thakur iterative procedure (as one of iterative methods) for the complex sine Tc(z)=asin(zr)+bz+c and complex exponential Tc(z)=aezr+bz+c functions. In order to obtain the fixed point of a complex-valued sine and exponential function, our concern is to use the fewest number of iterations possible. Using MATHEMATICA 13.0, some enticing and intriguing fractals are generated, and their behavior is then illustrated using graphical examples; this is achieved depending on the iteration parameters, the parameters ‘a’ and ‘b’, and the parameters involved in the series expansion of the sine and exponential functions.

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Dynamics of Julia Sets for Complex Exponential Functions

Cited by 6 publications

References 12 publications

A Brief Study on Julia Sets in the Dynamics of Entire Transcendental Function Using Mann Iterative Scheme

A Brief Study on Julia Sets in the Dynamics of Entire Transcendental Function Using Mann Iterative Scheme

STABILITY AND LYAPUNOV EXPONENTS OF A $q$-DEFORMED MAP

Mandelbrot and Julia Sets of Transcendental Functions Using Picard–Thakur Iteration

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