Study of Cubic Julia Sets in NO
نویسندگان
چکیده
Julia sets are considered one of the most attractive fractals and have wide range of applications in science and engineering. In recent decades, Rani and Kumar [26], introduced the Julia sets in superior orbits with improved escape criterions for the cubic polynomials. Our goal in this paper is to study the Julia sets in Noor orbit for the cubic polynomials 3 z z mz n . It is interesting to see that few cubic Julia sets are akin to Christmas tree, Sikh Mythological Symbol Khanda and some other decorative pictures.
منابع مشابه
Cubic Superior Julia Sets
Bodil Branner and John Hubbard produced the first extensive study of iterated complex maps for cubic polynomials in Picard orbit [Acta Math., 160(3-4):1988, 143-206]. Since then few researchers worked on Julia sets for cubic polynomials. In 2004, Rani and Kumar [J. Korea Soc. Math. Educ. Ser. D; Research in Math. Educ., 8(4):2004, 261-277] studied cubic polynomials in superior orbit and gave im...
متن کاملMcmullen’s Root-finding Algorithm for Cubic Polynomials
We show that a generally convergent root-finding algorithm for cubic polynomials defined by C. McMullen is of order 3, and we give generally convergent algorithms of order 5 and higher for cubic polynomials. We study the Julia sets for these algorithms and give a universal rational map and Julia set to explain the dynamics.
متن کاملJulia sets and Mandelbrot sets in Noor orbit
In recent literature, researchers have generated Julia sets and Mandelbrot sets in Mann and Ishikawa orbits that are examples of two-step and three-step feedback processes respectively. This paper presents further generalization of Julia and Mandelbrot sets for complex-valued polynomials such as quadratic, cubic and higher degree polynomials using a Noor orbit, which is a four-step iterative pr...
متن کاملPuiseux Series Polynomial Dynamics and Iteration of Complex Cubic Polynomials
We study polynomials with coefficients in a field L as dynamical systems where L is any algebraically closed and complete ultrametric field with dense valuation group and characteristic zero residual field. We give a complete description of the dynamical and parameter space of cubic polynomials. In particular we characterize cubic polynomials with compact Julia sets. Also, we prove that any inf...
متن کاملReal Analyticity of Hausdorff Dimension of Julia Sets of Parabolic Polynomials
We prove that D0, the set of all parameters λ ∈ C \ {0} for which the cubic polynomial fλ is parabolic and has no other parabolic or finite attracting periodic cycles, contains a deleted neighborhood of the origin 0. Our main result is that the function D0 3 λ 7→ HD(J(fλ)) ∈ R is real-analytic. This function ascribes to the polynomial fλ the Hausdorff dimension of its Julia set J(fλ). The theor...
متن کامل