数学博士后科研流动站 - 博士后出站报告（李长兵博士）

报告题目：The topological entropy dimension and variational relations of packing topological pressure for nonautonomous dynamical systems

报告人：李长兵 博士(汕头大学)

报告时间：2025年5月10日 9:30

报告地点：东海岸校区-D实232

摘要：The nonautonomous dynamical systems (NDS for short) is an extension of the classical dynamical systems. In contrast to the classical systems, the properties of NDS rely on a sequence of continuous selfmaps rather than a single one. This suggests that NDS possesses numerous analogous concepts and properties, including topological and measure-theoretic pressures, et al. Nevertheless, it has been demonstrated that certain results and techniques may not be applicable in NDS. In this presentation, we will share some recent studies on the topological entropy dimension and topological pressure for NDS. The present study investigates two types of topological entropy dimensions and various topological pressures, as well as the corresponding measure-theoretic pressures based on the Carathéodory-Pesin structure. We derive several properties of the topological entropy dimensions. These properties include the relationship between these topological entropy dimensions and the relationship between the topological entropy dimensions and the topological entropy. Concurrently, we establish a pressure distribution principle, a Bowen’s equation and a Billingsley type theorem for Pesin and packing topological pressure. Furthermore, we obtain a variational principle for packing topological pressure for NDS.