Zobrazeno 1 - 10
of 103
pro vyhledávání: '"Shen, Weixiao"'
Autor:
Ren, Haojie, Shen, Weixiao
For a real analytic periodic function $\phi:\mathbb{R}\to\mathbb{R}^d$, an integer $b \ge 2$ and $\lambda\in(1/b,1)$, we prove that the box dimension and the Hausdorff dimension of the graph of the Weierstrass function $W(x)=\sum_{n=0}^{\infty}{{\lam
Externí odkaz:
http://arxiv.org/abs/2404.06778
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:
Ji, Zhuchao, Shen, Weixiao
Wandering Fatou components were recently constructed by Astorg et al for higher dimensional holomorphic maps on projective spaces. Their examples are polynomial skew products with a parabolic invariant line. In this paper we study this wandering doma
Externí odkaz:
http://arxiv.org/abs/2209.01715
Autor:
Gao, Rui, Shen, Weixiao
In this paper, we prove that for real analytic expanding circle maps, all optimizing measures of a real analytic potential function have zero entropy, unless the potential is cohomologous to constant. We use the group structure of the symbolic space
Externí odkaz:
http://arxiv.org/abs/2206.05467
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:
Shen, Weixiao, Wang, Yimin
Using quasiconformal surgery, we prove that any primitive, postcritically-finite hyperbolic polynomial can be tuned with an arbitrary generalized polynomial with non-escaping critical points, generalizing a result of Douady-Hubbard for quadratic poly
Externí odkaz:
http://arxiv.org/abs/2010.05199
Autor:
Ren, Haojie, Shen, Weixiao
Publikováno v:
Inventiones Mathematicae (online 2021). A view-only version is available at https://rdcu.be/cpHDe
For a real analytic periodic function $\phi:\mathbb{R}\to \mathbb{R}$, an integer $b\ge 2$ and $\lambda\in (1/b,1)$, we prove the following dichotomy for the Weierstrass-type function $W(x)=\sum\limits_{n\ge 0}{{\lambda}^n\phi(b^nx)}$: Either $W(x)$
Externí odkaz:
http://arxiv.org/abs/2007.04312
Akademický článek
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Given an integer $q\ge 2$ and a real number $c\in [0,1)$, consider the generalized Thue-Morse sequence $(t_n^{(q;c)})_{n\ge 0}$ defined by $t_n^{(q;c)} = e^{2\pi i c S_q(n)}$, where $S_q(n)$ is the sum of digits of the $q$-expansion of $n$. We prove
Externí odkaz:
http://arxiv.org/abs/1903.09425
Publikováno v:
J. Anal. Math. 141 (2020), no. 1, 247-284
In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in \cite{LSvS1} to treat unfolding of critical relations can also be used to deal with cases where the critical orbi
Externí odkaz:
http://arxiv.org/abs/1901.09941