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Feng Rong

Publications and source records attributed to Feng Rong.

18 recordsLinked to original sources
arXiv2026

Dynamics inside the attracting basins of some skew products

Polynomial skew products in $\mathbb{C}^2$ are maps of the form $F(z,w)=(P(z),Q(z,w))$, where $P$ and $Q$ are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.

math.DS↗
arXiv2021

On the generalized squeezing functions and Fridman invariants of special domains

The main purpose of this paper is to study the generalized squeezing functions and Fridman invariants of some special domains. As applications, we give the precise form of generalized squeezing functions and Fridman invariants of various domains such as n-dimensional annuli. Furthermore, we provide domains with non-plurisubharmonic generalized squeezing function or Fridman invariant.

math.CV↗
arXiv2021

On Fridman invariants and generalized squeezing functions

In this paper, we introduce the notion of generalized squeezing function and study the basic properties of generalized squeezing functions and Fridman invariants. We also study the comparison of these two invariants, in terms of the so-called quotient invariant.

math.CV↗
arXiv2020

On the comparison of the Fridman invariant and the squeezing function

Let $D$ be a bounded domain in $\mathbb{C}^n$, $n\ge 1$. In this paper, we study two biholomorphic invariants on $D$, the Fridman invariant $e_D(z)$ and the squeezing function $s_D(z)$. More specifically, we study the following two questions about the \textit{quotient invariant} $m_D(z)=s_D(z)/e_D(z)$: 1) If $m_D(z_0)=1$ for some $z_0\in D$, is $D$ biholomorphic to the unit ball? 2) Is $m_D(z)$ constantly equal to 1? We answer both questions negatively.

math.CV↗
arXiv2016

On biholomorphisms between bounded quasi-Reinhardt domains

In this paper, we define what is called a quasi-Reinhardt domain and study biholomorphisms between such domains. We show that all biholomorphisms between two bounded quasi-Reinhardt domains fixing the origin are polynomial mappings, and we give a uniform upper bound for the degree of such polynomial mappings. In particular, we generalize the classical Cartan's linearity theorem for circular domains to quasi-Reinhardt domains.

math.CV↗
arXiv2015

On automorphisms of quasi-circular domains fixing the origin

It is known that automorphisms of quasi-circular domains fixing the origin are polynomial mappings. By introducing the so-called resonance order and quasi-resonance order, we provide a uniform upper bound for the degree of such polynomial automorphisms. As a particular consequence of our result, we obtain a generalization of the classical Cartan's theorem for circular domains to the quasi-circular case.

math.CV↗
arXiv2013

The Briot-Bouquet systems and the center families for holomorphic dynamical systems

We give a complete solution to the existence of isochronous center families for holomorphic dynamical systems. The study of center families for n-dimensional holomorphic dynamical systems naturally leads to the study of (n-1)-dimensional Briot-Bouquet systems in the phase space. We first give a detailed study of the Briot-Bouquet systems. Then we show the existence of isochronous center families in the neighborhood of the equilibrium point of three-dimensional systems based on the two-dimensional Briot-Bouquet theory. The same approach works in arbitrary dimensions.

math.DS↗
arXiv2012

Dynamics of quasi-parabolic one-resonant biholomorphisms

In this paper we study the dynamics of germs of quasi-parabolic one-resonant biholomorphisms of $\C^{n+1}$ fixing the origin, namely, those germs whose differential at the origin has one eigenvalue 1 and the others having a one dimensional family of resonant relations. We define some invariants and give conditions which ensure the existence of attracting domains for such maps.

math.CV↗
arXiv2006

Attractors on $\mathbf{P}^k$

We show that special perturbations of a particular holomorphic map on $\mathbf{P}^k$ give us examples of maps that possess chaotic nonalgebraic attractors. Furthermore, we study the dynamics of the maps on the attractors. In particular, we construct invariant hyperbolic measures supported on the attractors with nice dynamical properties.

math.DS↗
arXiv2006

The Fatou Set for Critically Finite Maps

It is a classical result in complex dynamics of one variable that the Fatou set for a critically finite map on $\mathbf{P}^1$ consists of only basins of attraction for superattracting periodic points. In this paper we deal with critically finite maps on $\mathbf{P}^k$. We show that the Fatou set for a critically finite map on $\mathbf{P}^2$ consists of only basins of attraction for superattracting periodic points. We also show that the Fatou set for a $k-$critically finite map on $\mathbf{P}^k$ is empty.

math.DS↗