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...

Gao, Yan

In this paper, we define the core entropy for postcritically-finite Newton maps and study its continuity within this family. We show that the entropy function is not continuous in this family, which is different from the polynomial case studied by Thurston, Gao, Dudko-Schleicher, Tiozzo [Th+, GT, DS, Ti2], and describe completely the continuity of ...

Cordero, Alicia Jaiswal, Jai P. Torregrosa, Juan R.
Published in
Applied Mathematics and Nonlinear Sciences

The use of complex dynamics tools in order to deepen the knowledge of qualitative behaviour of iterative methods for solving non-linear equations is a growing area of research in the last few years with fruitful results. Most of the studies dealt with the analysis of iterative schemes for solving non-linear equations with simple roots; however, the...

Dupont, Christophe Taflin, Johan

We study the structure and the Lyapunov exponents of the equilibrium measure of endomorphisms of $\mathbb P^k$ preserving a fibration. We extend the decomposition of the equilibrium measure obtained by Jonsson for polynomial skew products of $\mathbb C^2$. We also show that the sum of the sectional exponents satisfies a Bedford-Jonsson formula when...

Blokh, Alexander Oversteegen, Lex Timorin, Vladlen
Published in
Science China Mathematics

The combinatorial Mandelbrot set is a continuum in the plane, whose boundary is defined as the quotient space of the unit circle by an explicit equivalence relation. This equivalence relation was described by Douady (1984) and, separately, by Thurston (1985) who used quadratic invariant geolaminations as a major tool. We showed earlier that the com...

Floyd, William J. Parry, Walter R. Pilgrim, Kevin M.
Published in
Science China Mathematics

Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps, we investigate relationships between various notions of expansion—combinatorial, dynamical, algebraic, and coarse-geometric.

Qiu, Weiyuan Yang, Fei Yin, Yongcheng
Published in
Science China Mathematics

We study the quasisymmetric geometry of the Julia sets of McMullen maps fλ(z) = zm + λ/zℓ, where λ ∈ ℂ {0} and ℓ and m are positive integers satisfying 1/ℓ+1/m