Non-renormalizable Newton maps are rigid.More precisely,we prove that their Julia sets carry no invariant line fields and that a topological conjugacy between them is equivalent to a quasiconformal conjugacy.
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...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,and describe completely the continuity of the entropy function at the generic parameters.展开更多
In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed poin...In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed point determination, stability analysis and measure of the mean convergence time, which is confirmed by our analytical convergence time model. Stability of solutions is confirmed by measuring the Lyapunov exponent over the parameter space of each map. A generalization of the second map is proposed, giving rise to a family of new maps to address the same problem. This work is developed within the language of discrete dynamical systems.展开更多
基金supported by National Natural Science Foundation of China(Grants Nos.12131016 and 12271115)the Fundamental Research Funds for the Central Universities(Grant No.2021FZZX001-01)。
文摘Non-renormalizable Newton maps are rigid.More precisely,we prove that their Julia sets carry no invariant line fields and that a topological conjugacy between them is equivalent to a quasiconformal conjugacy.
基金supported by National Natural Science Foundation of China (Grant Nos.11871354 and 12131016)。
文摘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,and describe completely the continuity of the entropy function at the generic parameters.
文摘In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed point determination, stability analysis and measure of the mean convergence time, which is confirmed by our analytical convergence time model. Stability of solutions is confirmed by measuring the Lyapunov exponent over the parameter space of each map. A generalization of the second map is proposed, giving rise to a family of new maps to address the same problem. This work is developed within the language of discrete dynamical systems.
