2018年10月30日 14:00-18:00  闵行数学楼102报告厅

$(t_n^{(c)})_{n\ge 0}$, $c\in\R$ 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 that the maximum value is attained by a Sturmian measure. We also show that that $2^{-n} |\sigma_{2^n}(x)|$ 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.

Abstract: We consider the classical geometric Lorenz attractors, showing that the SRB entropy admits r-Holder continuity for any 0