Iteration operators on self-maps of locally compact Hausdorff spaces
报告专家： Chaitanya Gopalakrishna（ ISI Bangalore）
报告时间：2024年7月3日（星期三）下午15：00-16：00
报告地点：数学学院西303
报告摘要：The semi-dynamical system of a continuous self-map is generated by iteration of the map; however, the iteration itself, being an operator on the space of continuous self-maps, may generate interesting dynamical behaviors. In this talk we discuss some dynamical properties of the iteration operator on the space of continuous self-maps of a locally compact Hausdorff space. In particular, we characterize its fixed points and periodic points in the case that the locally compact Hausdorff space is a compact interval by discussing the Babbage equation. We prove that all orbits of the iteration operator are bounded, yet most of the fixed points are unstable. The boundedness and the instability exhibit the complexity of the system, but we show that the complicated behavior is not Devaney chaotic. The talk is based on our recent works [1, 2].
[1] Chaitanya Gopalakrishna, Murugan Veerapazham and Weinian Zhang, Dynamics of iteration operators on self-maps of locally compact Hausdorff spaces, Ergodic Theory Dynam. Systems, 44(3) (2024), 749–768.
[2] Murugan Veerapazham, Chaitanya Gopalakrishna and Weinian Zhang, Dynamics of the iteration operator on the space of continuous self-maps, Proc. Amer. Math. Soc., 147(1) (2021), 217–229.
专家简介：Chaitanya Gopalakrishna博士是印度统计研究所的INSPIRE教师研究员，其主要研究方向为动力系统和泛函方程。他主要探讨了连续自映射空间上的非迭代点密集性问题、迭代算子的动力学行为，以及映射的揉捏矩阵与其迭代之间的关系。他的研究成果发表在 Proc. Amer. Math. Soc.、 Nonlinearity、 Ergodic Theory Dynam. Systems、 Aequationes Math. 等知名数学期刊上。
邀请人：张伟年