Title 1: Asymptotic behaviors of generalized Thue-More Trigonometric polynomials
Speaker: Pro.Weixiao Shen(Fudan University)
Time: Fri, Dec.7, 2018 , AM:9:00-10:00
Location: Room 4141, Building No.4, Wushan Campus
Abstract：
Generalized Thue-Morse sequences are defined by $(t_n^{(c)})_{n\ge 0}$, $c\in\R$ being a parameter, by $t_n^{(c)}=e^{2\pi c S_2(n)}$,where $S_2(n)$ is the sum of digits of the binary expansion of $n$.The polynomials $\sigma_{N}^{(c)}(x) =\sum_{n=0}^{N-1} t_n^{(c)}e^{2\pi i x}$ are studied.
We prove that the uniform norm $\|\sigma_N^{(c)}\|_\infty$ behaves like $N^{\gamma(c)}$, and the exponent is the dynamical maximal value of $\log | \cos \pi (x+c)|$ relative to the doubling dynamics $x \mapsto 2x \mod 1$ and thatthe maximum value is attained by a Sturmian measure. We also show thatthat $2^{-n} |\sigma_{2^n}(x)|$ behaves like $e^{n\alpha(x)}$ with $\alpha(x) < 0$ and that the function $\alpha(x)$ is multifractal. This is a joint work with Fan and Schmeling.
Title 2: Stable Sets and Chaos in Positive Entropy Systems
Speaker: Pro.Wen Huang(University of Science and Technology of China)
Time: Fri, Dec.7, 2018 , AM:10:05-11:05
Location: Room 4141, Building No.4, Wushan Campus
Abstract：
In this talk, I will present the chaotic phenomenon of a dynamical system with positive entropy. It is shown that a dynamical system has positive entropy if and only if it has a weak horseshoe. Particularly, I will show that a Lorentz attractor has a weak horseshoe. Moreover, I will present the Hausdorff dimension and the chaotic behavior of stable sets and unstable sets in a C1-diffeomorphism system with positive entropy. The lower bound of the Hausdorff dimension of these stable sets and unstable sets is given in terms of the metric entropy and the largest Lyapunov exponent.
Title 3: Construction of Fractal Interpolation Function and Box-counting Dimension
Speaker: Pro.Huojun Ruan(Zhejiang University)
Time: Fri, Dec.7, 2018 , AM:11:10-12:00
Location: Room 4141, Building No.4, Wushan Campus
Abstract：
Fractal interpolation function was introduced by Barnsley in 1986,and we will briefly introduce its construction and box-counting dimension formula.
