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2018年10月30日 14:00-18:00  闵行数学楼102报告厅

题目: Asymptotic behaviors of generalized Thue-More Trigonometric polynomials.
报告人: 沈维孝教授(复旦大学上海数学中心首席教授)
摘要: 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 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.

题目:Topological pressure and its applications in dimension theory
摘要: In this talk, we will give some recent results in the dimension theory of dynamical systems, with emphasis on the applications of topological pressure in estimating the dimension of repellers and hyperbolic sets and the dimension of invariant measures. In the case of conformal dynamics, the theory is completely well understood. However, it still lacks today a satisfactory general approach for the non-conformal case, although a number of interesting and nontrivial developments obtained. Indeed, we only well understand some particular non-conformal repellers, e.g., generalized Sierpi?nski carpets and average conformal repellers.

报告题目:Regularity of SRB entropy for geometric Lorenz attractors
报告人: 廖刚教授( 苏州大学)。
Abstract: We consider the classical geometric Lorenz attractors, showing that the SRB entropy admits r-Holder continuity for any 0

报告题目:Comparison property for group actions
报告人: 张国华教授 (复旦大学,国家自然科学优秀青年基金获得者)
摘要:Let a countable amenable group G act on a zero-dimensional compact metric space X. We say that the action admits comparison if for any clopen sets A and B, the condition, that for every G-invariant measure m on X we have the sharp inequality m(A)< m(B), implies that A is subequivalent to B, that is, there exists a finite clopen partition A1, ..., Ak for A, and elements g1, ..., gk in G such that g1(A1), ..., gk(Ak) are disjoint clopen subsets of B. We prove this property for actions of groups whose every finitely generated subgroup has subexponential growth. This is a joint work with Professor Tomasz Downarowicz.