标题： 拓扑熵增长的机制以及混沌吸引子形状全局变化 显示英文标题

标题： A mechanism for growth of topological entropy and global changes of the shape of chaotic attractors

摘要： 拓扑熵的关键概念的理论和数值理解是动力系统中的一个重要问题。大多数研究都是针对映射（离散时间系统）进行的。我们分析了连续时间系统中吸引子结构全局变化的一个场景，导致基础动力系统的拓扑熵呈无界增长。作为示例，我们考虑经典的罗素系统。我们证明对于参数的一个明确范围，存在混沌吸引子。我们还证明了一连串导致拓扑熵增长的分岔的存在。这些证明是计算机辅助的。 显示英文摘要

摘要： The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes of the structure of an attractor in continuous-time systems leading to an unbounded growth of the topological entropy of the underlying dynamical system. As an example, we consider the classical Roessler system. We show that for an explicit range of parameters a chaotic attractor exists. We also prove the existence of a sequence of bifurcations leading to the growth of the topological entropy. The proofs are computer-aided.