Zobrazeno 1 - 10
of 183
pro vyhledávání: '"Fan, Aihua"'
On any finite algebraic extension $K$ of the field $\Q_p$ of $p$-adic numbers, there exist rational maps $\phi\in K(z)$ such that dynamical system $(\mathbb{P}^{1}(K),\phi)$ has empty Fatou set, i.e. the iteration family $\{\phi^n: n\geq 0\}$ is nowh
Externí odkaz:
http://arxiv.org/abs/2401.06314
This paper is a complement to our previous paper [21]. It surveys the works on the Furstenberg set $S=\{2^{m}3^{n}: n\ge 0, m\ge 0\}$ and its random version $T$. We also present some new results. For example, it is proved that $T$ almost surely conta
Externí odkaz:
http://arxiv.org/abs/2303.06850
We consider the generalized Thue-Morse sequences $(t_n^{(c)})_{n\ge 0}$ ($c \in [0,1)$ being a parameter) defined by $t_n^{(c)} = e^{2\pi i c s_2(n)}$, where $s_2(n)$ is the sum of digits of the binary expansion of $n$. For the polynomials $\sigma_{N
Externí odkaz:
http://arxiv.org/abs/2212.13234
Autor:
Fan, Aihua, Wu, Meng
Let $A(x): =(A_{i, j}(x))$ be a continuous function defined on some subshift of $\Omega:= \{0,1, \cdots, m-1\}^\mathbb{N}$, taking $d\times d$ non-negative matrices as values and let $\nu$ be an ergodic $\sigma$-invariant measure on the subshift wher
Externí odkaz:
http://arxiv.org/abs/2212.12890
We study some number-theoretic, ergodic and harmonic analysis properties of the Furstenberg set of integers $S=\{2^{m}3^{n}\}$ and compare them to those of its random analogue $T$. In this half-expository work, we show for example that $S$ is "Khinch
Externí odkaz:
http://arxiv.org/abs/2104.08944
Autor:
Fan, Aihua, Meyer, Yve
The random trigonometric series $\sum_{n=1}^\infty \rho_n \cos (nt +\omega_n)$ on the circle $\mathbb{T}$ are studied under the conditions $\sum |\rho_n|^2=\infty$ and $\rho_n\to 0$, where $\{\omega_n\}$ are iid and uniformly distributed on $\mathbb{
Externí odkaz:
http://arxiv.org/abs/2104.02524
For a continuous $\mathbb{N}^d$ or $\mathbb{Z}^d$ action on a compact space, we introduce the notion of Bohr chaoticity, which is an invariant of topological conjugacy and which is proved stronger than having positive entropy. We prove that all princ
Externí odkaz:
http://arxiv.org/abs/2103.04767
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 conjecture. We prove the Bohr chaoticity for all systems which have a horseshoe
Externí odkaz:
http://arxiv.org/abs/2103.04745
Autor:
Li, Chaosi1 (AUTHOR) lichaosi14@163.com, Fan, Aihua1 (AUTHOR) fiona.fan@boehringer-ingelheim.com, Liu, Zhicheng2,3 (AUTHOR) rainman136@aliyun.com, Wang, Gang4 (AUTHOR) wg0381@163.com, Zhou, Lei5,6 (AUTHOR) leosj@cau.edu.cn, Zhang, Hongliang7 (AUTHOR) zhanghongliang01@caas.cn, Huang, Lv1 (AUTHOR), Zhang, Jianfeng2 (AUTHOR) 13668939298@139.com, Zhang, Zhendong8 (AUTHOR) zhangzhend90@126.com, Zhang, Yan9 (AUTHOR) zhangyanyan008@163.com
Publikováno v:
Viruses (1999-4915). May2024, Vol. 16 Issue 5, p774. 15p.
Autor:
Fan, Aihua
We propose to study the multifractal behavior of weighted ergodic averages. Our study in this paper is concentrated on the symbolic dynamics. We introduce a thermodynamical formalism which leads to a multifractal spectrum. It is proved that this ther
Externí odkaz:
http://arxiv.org/abs/2004.03795