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

2008 ◽  
Vol 97 (3) ◽  
pp. 599-622 ◽  
Author(s):  
Núria Fagella ◽  
Xavier Jarque ◽  
Jordi Taixés
Keyword(s):  
Fixed Points ◽  
Julia Sets ◽  
Meromorphic Maps

scholarly journals On connectivity of Julia sets of transcendental meromorphic maps and weakly repelling fixed points II

2011 ◽  
Vol 215 (2) ◽  
pp. 177-202 ◽  
Author(s):  
Núria Fagella ◽  
Xavier Jarque ◽  
Jordi Taixés
Keyword(s):  
Fixed Points ◽  
Julia Sets ◽  
Meromorphic Maps

FIXED POINTS-JULIA SETS

2020 ◽  
Vol 9 (9) ◽  
pp. 6759-6763
Author(s):  
G. Subathra ◽  
G. Jayalalitha
Keyword(s):  
Fixed Points ◽  
Julia Sets

Dynamics of a family of orbitally continuous mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3507-3517
Author(s):  
Abhijit Pant ◽  
R.P. Pant ◽  
Kuldeep Prakash
Keyword(s):  
Fixed Points ◽  
Julia Sets ◽  
Real Numbers ◽  
Continuous Mappings ◽  
Non Linear

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.

Böttcher coordinates at fixed indeterminacy points

2018 ◽  
Vol 39 (12) ◽  
pp. 3437-3456 ◽  
Author(s):  
KOHEI UENO
Keyword(s):  
Fixed Points ◽  
Skew Products ◽  
Open Set ◽  
Monomial Map ◽  
Meromorphic Maps

We first consider the dynamics of a class of meromorphic skew products having superattracting fixed points or fixed indeterminacy points at the origin. Our theorem asserts that, if a map has a suitable weight, then it is conjugate to the associated monomial map on an invariant open set whose closure contains the origin. We next extend this result to a wider class of meromorphic maps such that the eigenvalues of the associated matrices are real and greater than $1$.

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

2019 ◽  
Vol 3 (3) ◽  
pp. 42 ◽  
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.

INFINITE BASINS OF JULIA SETS

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.

scholarly journals Index theorems for meromorphic self-maps of the projective space

2014 ◽  
Author(s):  
Marco Abate
Keyword(s):  
Line Bundle ◽  
Projective Space ◽  
Fixed Points ◽  
Index Theorem ◽  
Connected Components ◽  
Small Letter ◽  
Index Theorems ◽  
Dimensional Projective Space ◽  
Meromorphic Maps ◽  
Tangent To The Identity

This chapter uses techniques from the theory of local dynamics of holomorphic germs tangent to the identity to prove three index theorems for global meromorphic maps of projective space. More precisely, the chapter seeks to prove a particular index theorem: Let f : ℙⁿ ⇢ ℙⁿ be a meromorphic self-map of degree ν‎ + 1 ≥ 2 of the complex n-dimensional projective space. Let Σ‎(f) = Fix(f) ∪ I(f) be the union of the indeterminacy set I(f) of f and the fixed points set Fix(f) of f. Let Σ‎(f) = ⊔subscript Greek Small Letter AlphaΣ‎subscript Greek Small Letter Alpha be the decomposition of Σ‎ in connected components, and denote by N the tautological line bundle of ℙⁿ. After laying out the statements under this theorem, the chapter discusses the proofs.

CHAOS AND FRACTALS IN C–K MAP

2008 ◽  
Vol 19 (09) ◽  
pp. 1389-1409 ◽  
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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