报告题目： The structure of optimal orbit: simple vs sophisticated 

报告人：张一威，华中科技大学

时间：2021年1月19日（周二）下午4：00-5：00

地点：东区第五教学楼5306教室

摘要： Given a topological dynamical system $T:X\to X$, and an continuous observable $\varphi:X\to\mathbb{R}$, we say an orbit $\mathcal{O}_{x_{0}}=\{x_{0},T(x_{0}),\cdots\}$ is an $f$-optimal orbit, if the Birkhoff average $\langle\varphi\rangle(x_{0}):=\lim_{n\to\infty}\frac{1}{n}\varphi(T^{i}(x_{0}))$ exists, and $\langle\varphi\rangle(x_{0})\geq\limsup_{n\to\infty}\frac{1}{n}\varphi(T^{i}(x)),\forall x\in X$, and define by $\mathcal{S}_{op}\subset X$, the set of initial states, which give rise to the optimal orbit.  We will investigate the geometric structure of $\mathcal{S}_{op}$, and see how $\mathcal{S}_{op}$ varies, corresponding to the variances on the hyperbolicity of $T$, and regularity of $\varphi$. 

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