Aihua Fan

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20242026

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math.DS2026

A Weyl-type theorem for Diophantine approximations driven by LCA groups and applications

Aihua Fan

We investigate actions of locally compact Abelian (LCA) groups on the torus $T^{n}$ , motivated by their close connection with Diophantine approximation. While Kronecker's th…

math.DS2026

Khintchin conjecture and related topics

Aihua Fan, Shilei Fan, Hervé Queffélec +1

Motivated by Khintchin's 1923 conjecture, refuted by Marstrand in 1970, we study the Khintchin class of functions associated to a given increasing sequence of integers. When the Kh…

math.DS2025

Computation of Lyapunov exponents of matrix products

Aihua Fan, Evgeny Verbitskiy

For $m$ given square matrices $A_{0}, A_{1}, \dots, A_{m - 1}$ ( $m \geq 2$ ), one of which is assumed to be of rank $1$ , and for a given sequence $(ω_{n})$ in $\{0,1, \cdots, m-1\}^\mathbb{N…

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…

A Weyl-type theorem for Diophantine approximations driven by LCA groups and applications

Khintchin conjecture and related topics

Computation of Lyapunov exponents of matrix products

p-adic rational maps having empty Fatou set

$p$ -adic rational maps having empty Fatou set