Chen, Jinchao Li, Yezhou Wu, Chengfa
Published in
Mediterranean Journal of Mathematics

In this paper, entire solutions f of a class of nonlinear difference equations are studied. By considering the order and deficiency of the coefficients in the equations, we investigate the properties of the radial distribution of the Julia set of f, and estimate the lower bound of the measure of the set defined by the common limiting directions of ...

Brame, Micah Kaschner, Scott
Published in
Complex Analysis and its Synergies

For maps of one complex variable, f, given as the sum of a degree n power map and a degree d polynomial, we provide necessary and sufficient conditions that the geometric limit as n approaches infinity of the set of points that remain bounded under iteration by f is the closed unit disk or the unit circle. We also provide a general description, for...

Zhang, Yuhan Gao, Junyang Qiao, Jianyong Wang, Qinghua
Published in
Frontiers of Mathematics in China

Considering a family of rational maps Tnλ concerning renormalization transformation, we give a perfect description about the dynamical properties of Tnλ and the topological properties of the Fatou components F(Tnλ). Furthermore, we discuss the continuity of the Hausdorff dimension HD(J(Tnλ)) about real parameter λ.

Mishra, Vishnu Narayan Tomar, Garima
Published in
Mathematica Slovaca

Dynamics of composition of entire functions is well related to it's factors, as it is known that for entire functions f and g, fog has wandering domain if and only if gof has wandering domain. However the Fatou components may have different structures and properties. In this paper we have shown the existence of domains with all possibilities of wan...

Huang, Xiaojie Qiu, Weiyuan
Published in
Chinese Annals of Mathematics, Series B

It is proved in this paper that the union of escaping parameter rays without endpoints for the cosine family Sκ (z) = eκ(ez + e−z), where κ ∈ ℂ is a parameter, has Hausdorff dimension 1, which implies that the ray endpoints alone have Hausdorff dimension 2. This shows that Karpińska’s dimension paradox occurs also in the parameter plane of the cosi...

Cao, Chunlei Wang, Yuefei
Published in
Acta Mathematica Scientia

In 1965 Baker first considered the distribution of Julia sets of transcendental entire maps and proved that the Julia set of an entire map cannot be contained in any finite set of straight lines. In this paper we shall consider the distribution problem of Julia sets of meromorphic maps. We shall show that the Julia set of a transcendental meromorph...

Tomar, Garima Mishra, Vishnu Narayan
Published in
Mathematica Slovaca

Levels of fast escaping sets were discussed by Rippon and Stallard. Here we have defined a set BR(f) analogous to 0th level of fast escaping set by using maximum term and formation of spider’s web structure has been discussed for this set.

Liu, Tianbao Qin, Xiwen Li, Qiuyue
Published in
Open Mathematics

In this paper, we derive and analyze a new one-parameter family of modified Cauchy method free from second derivative for obtaining simple roots of nonlinear equations by using Padé approximant. The convergence analysis of the family is also considered, and the methods have convergence order three. Based on the family of third-order method, in orde...

Gao, Yan Zeng, Jinsong
Published in
Science China Mathematics

Based on the distortion theory developed by Cui and Tan (2015), we prove the landing of every parameter ray at critical portraits coming from non-recurrent polynomials, thereby generalizing a result of Kiwi (2005).

Ding, Jie Wang, Jun Ye, Zhuan
Published in
Chinese Annals of Mathematics, Series B

The authors study a family of transcendental entire functions which lie outside the Eremenko-Lyubich class in general and are of infinity growth order. Most importantly, the authors show that the intersection of Julia set and escaping set of these entire functions has full Hausdor. dimension. As a by-product of the result, the authors also obtain t...