Shilei Fan

activity

20132026

Q_{p}

6 citations · 17 across the 18 of their papers we have counts for

collaborators

19 papers

math.CA2026

Lower bounds for parameter-dependent oscillatory integrals and Fourier frames on hypersurfaces

Shilei Fan, Bochen Liu

We prove lower bounds for Fourier transforms of surface measures $$|\widehat{ψ\,dσ}(ξ)| \gtrsim_{ψ, K, σ, R_0} σ(B(p, |ξ|^{-1})), \text{ given }p\in K\Subset\{ψ>0\} ,\ \vec{n}_{p}\…

math.DS2024

Expanding property and statistical laws for $p$ -adic subhyperbolic rational maps

Shilei Fan, Lingmin Liao, Hongming Nie +1

Let $K$ be a finite extension of the field $Q_{p}$ of $p$ -adic numbers. A rational map $ϕ \in K (z)$ of degree at least $2$ is subhyperbolic if each critical point in the $\ma…

math.DS2024

$p$ -adic rational maps having empty Fatou set

Aihua Fan, Shilei Fan, Yahia Mwanis +1

On any finite algebraic extension $K$ of the field $\Q_p$ of $p$ -adic numbers, there exist rational maps $ϕ \in K (z)$ such that dynamical system $(P^{1} (K), ϕ)$ has empty Fa…

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.DS2021★ 1 cited

Bohr chaoticity of topological dynamical systems

Aihua Fan, Shilei Fan, Valery Ryzhikov +1

We introduce the notion of Bohr chaoticity, which is a topological invariant for topological dynamical systems, and which is opposite to the property required by Sarnak's conjectur…

math.PR2019

Stationary determinantal processes: $ψ$ -mixing property and $L^{q}$ -dimensions

Shilei Fan, Lingmin Liao, Yanqi Qiu

The results of this paper are 3-folded. Firstly, for any stationary determinantal process on the integer lattice, induced by strictly positive and strictly contractive involution k…

math.PR2017★ 1 cited

Some properties of stationary determinantal point processes on $Z$

Ai-hua Fan, Shi-lei Fan, Yan-qi Qiu

We study properties of stationary determinantal point processes $\X$ on $Z$ from different points of views. It is proved that $\X\cap \N$ is almost surely Bohr-dense and good univ…

math.DS2017

Rational map ax+1/x on the projective line over $Q_{2}$

Shilei Fan, Lingmin Liao

The dynamical structure of the rational map $a x + 1/ x$ on the projective line over the field Q2 of $2$ -adic numbers, is fully described.

math.PR2017★ 2 cited

Equivalence of Palm measures for determinantal point processes governed by Bergman kernels

Alexander I. Bufetov, Shilei Fan, Yanqi Qiu

For a determinantal point process induced by the reproducing kernel of the weighted Bergman space $A^{2} (U, ω)$ over a domain $U \subset C^{d}$ , we establish the mutual absolu…

math.DS2017

Invariant measures for the actions of the modular group

Shilei Fan, Yanqi Qiu

In this note, we give a nature action of the modular group on the ends of the infinite (p + 1)-cayley tree, for each prime p. We show that there is a unique invariant probability m…

math.DS2016

Rational map $a x + 1/ x$ on the projective line over $Q_p$

Shilei Fan, Lingmin Liao

The dynamical structure of the rational map $a x + 1/ x$ on the projective line $¶$ over the field $Q_p$ of $p$ -adic numbers is described for $p \geq 3$ .

math.CA2015★ 6 cited

Fuglede's conjecture holds in $Q_{p}$

Aihua Fan, Shilei Fan, Lingmin Liao +1

Fuglede's conjecture in $Q_{p}$ is proved. That is to say, a Borel set of positive and finite Haar measure in $Q_{p}$ is a spectral set if and only if it tiles $\math…

math.DS2015

Dynamics of Chebyshev polynomials on $Z_{2}$

Shilei Fan, Lingmin Liao

The dynamical structure of Chebyshev polynomials on $Z_{2}$ , the ring of $2$ -adic integers, is fully described by showing all its minimal subsystems and their attracting bas…

math.NT2015★ 2 cited

Bounded tiles in $Q_{p}$ are compact open sets

Aihua Fan, Shilei Fan

Any bounded tile of the field $Q_{p}$ of $p$ -adic numbers is a compact open set up to a zero Haar measure set. In this note, we give a simple and direct proof of this fact.

math.DS2015

Minimality of p-adic rational maps with good reduction

Ai-Hua Fan, Shilei Fan, Lingmin Liao +1

A rational map with good reduction in the field $Q_p$ of $p$ -adic numbers defines a $1$ -Lipschitz dynamical system on the projective line $P^{1} (Q_p)$ ov…

math.FA2015★ 2 cited

Compact Open Spectral Sets In $Q_{p}$

Aihua Fan, Shilei Fan, Ruxi Shi

In this article, we prove that a compact open set in the field $Q_{p}$ of $p$ -adic numbers is a spectral set if and only if it tiles $Q_{p}$ by translation, and also…

math.DS2014★ 1 cited

Dynamics of the square mapping on the ring of $p$ -adic integers

Shilei Fan, Lingmin Liao

For each prime number $p$ , the dynamical behavior of the square mapping on the ring $Z_{p}$ of $p$ -adic integers is studied. For $p = 2$ , there are only attracting fixed point…

math.DS2014★ 1 cited

Dynamics of convergent power series on the integral ring of a finite extension of $\Qp$

Shilei Fan, Lingmin Liao

Let $K$ be a finite extension of the field $Q_{p}$ of $p$ -adic numbers and $Ø$ be its integral ring. The convergent power series with coefficients in $Ø$ are studied as dyna…

math.DS2013★ 1 cited

On minimal decomposition of $p$ -adic homographic dynamical systems

Aihua Fan, Shilei Fan, Lingmin Liao +1

A homographic map in the field of $p$ -adic numbers $\mathbb{Q}_p}$ is studied as a dynamical system on $P^{1} (Q_{p})$ , the projective line over $Q_{p}$ . If s…

Lower bounds for parameter-dependent oscillatory integrals and Fourier frames on hypersurfaces

Expanding property and statistical laws for p-adic subhyperbolic rational maps

p-adic rational maps having empty Fatou set

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

Bohr chaoticity of topological dynamical systems

Stationary determinantal processes: ψ-mixing property and Lq-dimensions

Some properties of stationary determinantal point processes on Z

Rational map ax+1/x on the projective line over Q2​

Equivalence of Palm measures for determinantal point processes governed by Bergman kernels

Invariant measures for the actions of the modular group

Rational map ax+1/x on the projective line over Q_p

Fuglede's conjecture holds in Qp​

Dynamics of Chebyshev polynomials on Z2​

Bounded tiles in Qp​ are compact open sets

Minimality of p-adic rational maps with good reduction

Compact Open Spectral Sets In Qp​

Dynamics of the square mapping on the ring of p-adic integers

Dynamics of convergent power series on the integral ring of a finite extension of $\Qp$

On minimal decomposition of p-adic homographic dynamical systems

Expanding property and statistical laws for $p$ -adic subhyperbolic rational maps

$p$ -adic rational maps having empty Fatou set

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

Stationary determinantal processes: $ψ$ -mixing property and $L^{q}$ -dimensions

Some properties of stationary determinantal point processes on $Z$

Rational map ax+1/x on the projective line over $Q_{2}$

Rational map $a x + 1/ x$ on the projective line over $Q_p$

Fuglede's conjecture holds in $Q_{p}$

Dynamics of Chebyshev polynomials on $Z_{2}$

Bounded tiles in $Q_{p}$ are compact open sets

Compact Open Spectral Sets In $Q_{p}$

Dynamics of the square mapping on the ring of $p$ -adic integers

On minimal decomposition of $p$ -adic homographic dynamical systems