Lingmin Liao

activity

20082026

most citedUniform Diophantine approximation related to

b

-ary and

β

-expansions

29 citations · 149 across the 38 of their papers we have counts for

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33 papers · 1 filter

math.DS2026

Survivor Set of Gauss Map with a Hole at $1$

Cheng Liu, Lingmin Liao

Let $T$ be the Gauss map. For each $α \in [0, 1]$ , let $E (α)$ be the survivor set consisting of all $x \in [0, 1]$ whose orbit ${T^{k} (x) : k \geq 0}$ never enters the interval $(α, 1]$ . We…

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.DS2023

Quantitative recurrence properties for piecewise expanding maps on $[0, 1]^{d}$

Yubin He, Lingmin Liao

Let $T : [0, 1]^{d} \to [0, 1]^{d}$ be a piecewise expanding map with an absolutely continuous invariant measure $μ$ . Let ${H_{n}}$ be a sequence of hyperrectangles or hyperboloid…

math.DS2022★ 3 cited

Path-dependent shrinking targets in generic affine iterated function systems

Henna Koivusalo, Lingmin Liao, Ian Morris +1

We calculate the Hausdorff dimension of shrinking target sets of symbolic balls in generic affine iterated function systems with matrix norms bounded by $\frac{1}{2}$ . Relative to ea…

math.DS2022

Uniform approximation problems of expanding Markov maps

Yubin He, Lingmin Liao

Let $T : [0, 1] \to [0, 1]$ be an expanding Markov map with a finite partition. Let $μ_{ϕ}$ be the invariant Gibbs measure associated with a Hölder continuous potential $ϕ$ . In this pa…

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★ 7 cited

Odd-odd continued fraction algorithm

Dong Han Kim, Seul Bee Lee, Lingmin Liao

By using a jump transformation associated to the Romik map, we define a new continued fraction algorithm called odd-odd continued fraction, whose principal convergents are rational…

math.DS2018

On the shortest distance between orbits and the longest common substring problem

Vanessa Barros, Lingmin Liao, Jerome Rousseau

In this paper, we study the behaviour of the shortest distance between orbits and show that under some rapidly mixing conditions, the decay of the shortest distance depends on the…

math.DS2017★ 1 cited

Periodic $p$ -adic Gibbs measures of $q$ -states Potts model on Cayley tree: The chaos implies the vastness of $p$ -adic Gibbs measures

Mohd Ali Khameini Ahmad, Lingmin Liao, Mansoor Saburov

We study the set of $p$ -adic Gibbs measures of the $q$ -states Potts model on the Cayley tree of order three. We prove the vastness of the periodic $p$ -adic Gibbs measures for such…

math.DS2017★ 2 cited

Multifractal analysis of the Birkhoff sums of Saint-Petersburg potential

Dong Han Kim, Lingmin Liao, Michal Rams +1

Let $((0, 1], T)$ be the doubling map in the unit interval and $φ$ be the Saint-Petersburg potential, defined by $φ (x) = 2^{n}$ if $x \in (2^{- n - 1}, 2^{- n}]$ for all $n \geq 0$ . We consid…

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.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.DS2016★ 1 cited

Hausdorff dimension of weighted singular vectors

Lingmin Liao, Ronggang Shi, Omri N. Solan +1

Let $w = (w_{1}, w_{2})$ be a pair of positive real numbers with $w_{1} + w_{2} = 1$ and $w_{1} \geq w_{2}$ . We show that the set of $w$ -weighted singular vectors in $R^{2}$ has Hausdorff dimens…

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.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.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★ 7 cited

Upper and lower fast Khintchine spectra in continued fractions

Lingmin Liao, Michal Rams

For an irrational number $x \in [0, 1)$ , let $x = [a_1 (x), a_2 (x), \dots]$ be its continued fraction expansion. Let $ψ : N \to N$ be a function with $ψ(n)/n\…

math.DS2014★ 29 cited

Subexponentially increasing sums of partial quotients in continued fraction expansions

Lingmin Liao, Michal Rams

We investigate from a multifractal analysis point of view the increasing rate of the sums of partial quotients $S_n (x) = \sum_j = 1^{n} a_j (x)$ , where $x=[a\_1(x), a\_2(x), \cdots ]…

math.DS2014★ 29 cited

Uniform Diophantine approximation related to $b$ -ary and $β$ -expansions

Yann Bugeaud, Lingmin Liao

Let $b \geq 2$ be an integer and $\hv$ a real number. Among other results, we compute the Hausdorff dimension of the set of real numbers $ξ$ with the property that, for every suffic…

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…

math.DS2012

Inhomogeneous Diophantine approximation with general error functions

Lingmin Liao, Michal Rams

Let $\al$ be an irrational and $φ : N \to R^{+}$ be a function decreasing to zero. For any $\al$ with a given Diophantine type, we show some sharp estimations for the Hausdo…

math.DS2012★ 5 cited

On the fast Khintchine spectrum in continued fractions

Fan Ai-Hua, Lingmin Liao, Bao-Wei Wang +1

For $x \in [0, 1)$ , let $x = [a_{1} (x), a_{2} (x), ...]$ be its continued fraction expansion with partial quotients $a_{n} (x), n \geq 1$ . Let $ψ : N \to N$ be a functi…

math.DS2012★ 4 cited

Multifractal analysis of some multiple ergodic averages in linear Cookie-Cutter dynamical systems

Ai-Hua Fan, Lingmin Liao, Meng Wu

In this paper, we study the multiple ergodic averages of a locally constant real-valued function in linear Cookie-Cutter dynamical systems. The multifractal spectrum of these multi…

Survivor Set of Gauss Map with a Hole at 1

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

Quantitative recurrence properties for piecewise expanding maps on [0,1]d

Path-dependent shrinking targets in generic affine iterated function systems

Uniform approximation problems of expanding Markov maps

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

Odd-odd continued fraction algorithm

On the shortest distance between orbits and the longest common substring problem

Periodic p-adic Gibbs measures of q-states Potts model on Cayley tree: The chaos implies the vastness of p-adic Gibbs measures

Multifractal analysis of the Birkhoff sums of Saint-Petersburg potential

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

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

Hausdorff dimension of weighted singular vectors

Dynamics of Chebyshev polynomials on Z2​

Minimality of p-adic rational maps with good reduction

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

Upper and lower fast Khintchine spectra in continued fractions

Subexponentially increasing sums of partial quotients in continued fraction expansions

Uniform Diophantine approximation related to b-ary and β-expansions

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

On minimal decomposition of p-adic homographic dynamical systems

Inhomogeneous Diophantine approximation with general error functions

On the fast Khintchine spectrum in continued fractions

Multifractal analysis of some multiple ergodic averages in linear Cookie-Cutter dynamical systems

Survivor Set of Gauss Map with a Hole at $1$

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

Quantitative recurrence properties for piecewise expanding maps on $[0, 1]^{d}$

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

Periodic $p$ -adic Gibbs measures of $q$ -states Potts model on Cayley tree: The chaos implies the vastness of $p$ -adic Gibbs measures

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

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

Dynamics of Chebyshev polynomials on $Z_{2}$

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

Uniform Diophantine approximation related to $b$ -ary and $β$ -expansions

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