Hongming Nie

activity

20162023

most citedBoundedness of Hyperbolic Components of Newton Maps

4 citations · 13 across the 16 of their papers we have counts for

collaborators

16 papers

math.DS2023

Böttcher coordinates at wild superattracting fixed points

Hang Fu, Hongming Nie

Let $p$ be a prime number, let $g (x) = x^{p^{2}} + p^{r + 2} x^{p^{2} + 1}$ with $r \in Z_{\geq 0}$ , and let $ϕ (x) = x + O (x^{2})$ be the Böttcher coordinate satisfying $ϕ(g(x))=ϕ(x)^{p^{…

math.DS2022

The basin of infinity of tame polynomials

Jan Kiwi, Hongming Nie

Let $C_{v}$ be a characteristic zero algebraically closed field which is complete with respect to a non-Archimedean absolute value. We provide a necessary and sufficient con…

math.DS2022

Nonarchimedean Lyapunov exponents of polynomials

Hongming Nie

Let $K$ be an algebraically closed and complete nonarchimedean field with characteristic $0$ and let $f \in K [z]$ be a polynomial of degree $d \geq 2$ . We study the Lyapunov exponent…

math.DS2021

Julia sets and geometrically finite maps over finite extensions of the $p$ -adic field

Shilei Fan, Lingmin Liao, Hongmin Nie +1

Let $K$ be a finite extension of the field $Q_{p}$ of $p$ -adic numbers, and $ϕ \in K (z)$ be a rational map of degree at least $2$ . We prove that the $K$ -Julia set of $ϕ$ is t…

math.DS2020

Quantitative equidistribution of angles of multipliers

Yan Mary He, Hongming Nie

We study angles of multipliers of repelling cycles for hyperbolic rational maps in $C (z)$ . For a fixed $K ≫ 1$ , we show that almost all intervals of length $2 π / K$ in $(-π…

math.NT2020

Resultant measures and minimal resultant loci for non-archimedean polynomial dynamics

Hongming Nie, Yûsuke Okuyama

We compute the resultant measures for iterations $P^{j}$ , $j \geq 1$ , of a polynomial $P$ of degree $> 1$ on the $n$ -th level Trucco's trees $Γ_{n}$ , $n \geq 0$ , in the Berkovich projective…

math.DS2020★ 1 cited

A Riemannian metric on polynomial hyperbolic components

Yan Mary He, Hongming Nie

We introduce a Riemannian metric on certain hyperbolic components in the moduli space of degree $d \geq 2$ polynomials. Our metric is constructed by considering the measure-theoreti…

math.DS2019

Perturbations of graphs for Newton maps

Yan Gao, Hongming Nie

We study the convergence of graphs consisting of finitely many internal rays for degenerating Newton maps. We state a sufficient condition to guarantee the convergence. As an appli…

math.DS2019

Siegel disks of the tangent family

Weiwei Cui, Hongming Nie

We study Siegel disks in the dynamics of functions from the tangent family. In particular, we prove that a forward invariant Siegel disk is unbounded if and only if it contains at…

math.DS2019★ 4 cited

Bounded hyperbolic components of bicritical rational maps

Hongming Nie, Kevin M. Pilgrim

We prove that the hyperbolic components of bicritical rational maps having two distinct attracting cycles each of period at least two are bounded in the moduli space of bicritical…

math.DS2018★ 1 cited

Indeterminacy loci of iterate maps in moduli space

Jan Kiwi, Hongming Nie

The moduli space $rat_{d}$ of rational maps in one complex variable of degree $d \geq 2$ has a natural compactification by a projective variety $rat_{d}$ pr…

math.DS2018★ 4 cited

Boundedness of Hyperbolic Components of Newton Maps

Hongming Nie, Kevin M. Pilgrim

We investigate boundedness of hyperbolic components in the moduli space of Newton maps. For quartic maps, (i) we prove hyperbolic components possessing two distinct attracting cycl…

math.DS2018

Compactifications of the moduli spaces of Newton maps

Hongming Nie

We study various compactifications of moduli space of Newton maps. Mainly, we focus on GIT compactifiaction and Deligne-Mumford compactification. Then we explore the relations amon…

math.DS2018★ 3 cited

Iteration at the Boundary of Newton Maps

Hongming Nie

Let ${N_{t}}$ be a holomorphic family of degree $d \geq 3$ Newton maps. By studying the related Berkovich dynamics, we obtain an estimate of the weak limit of the maximal measures of…

math.DS2017

Indeterminacy Loci of Iterate Maps

Hongming Nie

We consider the indeterminacy locus $I (Φ_{n})$ of the iterate map $Φ_{n} : M_{d} - r i g h t a r r o w M_{d^{n}}$ , where $M_{d}$ is the GIT compactification of the moduli…

math.DS2016

Rescaling Limits in Non-Archimedean Dynamics

Hongming Nie

Suppose ${f_{t}}$ is an analytic one-parameter family of rational maps defined over a non-Archimedean field $K$ . We prove a finiteness theorem for the set of rescalings for $\{f_t\…

Böttcher coordinates at wild superattracting fixed points

The basin of infinity of tame polynomials

Nonarchimedean Lyapunov exponents of polynomials

Julia sets and geometrically finite maps over finite extensions of the p-adic field

Quantitative equidistribution of angles of multipliers

Resultant measures and minimal resultant loci for non-archimedean polynomial dynamics

A Riemannian metric on polynomial hyperbolic components

Perturbations of graphs for Newton maps

Siegel disks of the tangent family

Bounded hyperbolic components of bicritical rational maps

Indeterminacy loci of iterate maps in moduli space

Boundedness of Hyperbolic Components of Newton Maps

Compactifications of the moduli spaces of Newton maps

Iteration at the Boundary of Newton Maps

Indeterminacy Loci of Iterate Maps

Rescaling Limits in Non-Archimedean Dynamics

Julia sets and geometrically finite maps over finite extensions of the $p$ -adic field