FIXED POINTS-JULIA SETS

The aim of the present paper is to study the dynamics of a class of orbitally continuous non-linear mappings defined on the set of real numbers and to apply the results on dynamics of functions to obtain tests of divisibility. We show that this class of mappings contains chaotic mappings. We also draw Julia sets of certain iterations related to multiple lowering mappings and employ the variations in the complexity of Julia sets to illustrate the results on the quotient and remainder. The notion of orbital continuity was introduced by Lj. B. Ciric and is an important tool in establishing existence of fixed points.

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On connectivity of Julia sets of transcendental meromorphic maps and weakly repelling fixed points I

Proceedings of the London Mathematical Society ◽

10.1112/plms/pdn012 ◽

2008 ◽

Vol 97 (3) ◽

pp. 599-622 ◽

Cited By ~ 3

Author(s):

Núria Fagella ◽

Xavier Jarque ◽

Jordi Taixés

Keyword(s):

Fixed Points ◽

Julia Sets ◽

Meromorphic Maps

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Fiber Julia sets of polynomial skew products with super-saddle fixed points

Proceedings of the American Mathematical Society ◽

10.1090/proc/15345 ◽

2020 ◽

pp. 1

Author(s):

Shizuo Nakane

Keyword(s):

Fixed Points ◽

Julia Sets ◽

Skew Products

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Exploration of Filled-In Julia Sets Arising from Centered Polygonal Lacunary Functions

Fractal and Fractional ◽

10.3390/fractalfract3030042 ◽

2019 ◽

Vol 3 (3) ◽

pp. 42 ◽

Cited By ~ 2

Author(s):

L.K. Mork ◽

Trenton Vogt ◽

Keith Sullivan ◽

Drew Rutherford ◽

Darin J. Ulness

Keyword(s):

Fixed Points ◽

Parameter Space ◽

Rotational Symmetry ◽

Julia Sets ◽

Phase Rotation ◽

Mandelbrot Sets

Centered polygonal lacunary functions are a particular type of lacunary function that exhibit properties which set them apart from other lacunary functions. Primarily, centered polygonal lacunary functions have true rotational symmetry. This rotational symmetry is visually seen in the corresponding Julia and Mandelbrot sets. The features and characteristics of these related Julia and Mandelbrot sets are discussed and the parameter space, made with a phase rotation and offset shift, is intricately explored. Also studied in this work is the iterative dynamical map, its characteristics and its fixed points.

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INFINITE BASINS OF JULIA SETS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127408022330 ◽

2008 ◽

Vol 18 (10) ◽

pp. 3169-3173

Author(s):

FİGEN ÇİLİNGİR

Keyword(s):

Entire Function ◽

Fixed Points ◽

Newton’S Method ◽

Newton's Method ◽

Julia Sets ◽

Rational Functions ◽

Complex Parameter

The goal of this paper is to investigate the iterative behavior of a particular class of rational functions which arise from Newton's method applied to the entire function (z2 + c)eQ(z) where c is a complex parameter and Q is a nonconstant polynomial with deg(Q) ≤ 2. In particular, the basins of attracting fixed points will be described.

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CHAOS AND FRACTALS IN C–K MAP

International Journal of Modern Physics C ◽

10.1142/s0129183108012935 ◽

2008 ◽

Vol 19 (09) ◽

pp. 1389-1409 ◽

Cited By ~ 5

Author(s):

XING-YUAN WANG ◽

QING-YONG LIANG ◽

JUAN MENG

Keyword(s):

Power Spectrum ◽

Fixed Points ◽

Lyapunov Exponents ◽

Correlation Dimension ◽

Julia Sets ◽

Mandelbrot Set ◽

Parameter Plane ◽

Boundary Equation ◽

Mandelbrot Sets

The characteristic of the fixed points of the Carotid–Kundalini (C–K) map is investigated and the boundary equation of the first bifurcation of the C–K map in the parameter plane is given. Based on the studies of the phase graph, the power spectrum, the correlation dimension and the Lyapunov exponents, the paper reveals the general features of the C–K map transforming from regularity. Meanwhile, using the periodic scanning technology proposed by Welstead and Cromer, a series of Mandelbrot–Julia (M–J) sets of the complex C–K map are constructed. The symmetry of M–J set and the topological inflexibility of distributing of periodic region in the Mandelbrot set are investigated. By founding the whole portray of Julia sets based on Mandelbrot set qualitatively, we find out that Mandelbrot sets contain abundant information of structure of Julia sets.

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Measure of the Julia set of the Feigenbaum map with infinite criticality

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385709000340 ◽

2009 ◽

Vol 30 (3) ◽

pp. 855-875 ◽

Cited By ~ 2

Author(s):

GENADI LEVIN ◽

GRZEGORZ ŚWIA̧TEK

Keyword(s):

Stochastic Process ◽

Fixed Points ◽

Lebesgue Measure ◽

Julia Set ◽

Julia Sets ◽

Martingale Theory ◽

Hyperbolic Dimension

AbstractWe consider fixed points of the Feigenbaum (periodic-doubling) operator whose orders tend to infinity. It is known that the hyperbolic dimension of their Julia sets goes to 2. We prove that the Lebesgue measure of these Julia sets tend to zero. An important part of the proof consists in applying martingale theory to a stochastic process with non-integrable increments.

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