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.

翻译：拓扑熵作为动力系统中的核心概念，其理论与数值理解是该领域的重要课题。现有研究主要集中于映射（离散时间系统）。本文分析了连续时间系统中吸引子结构的全局变化场景，该场景导致底层动力系统的拓扑熵无界增长。以经典Rössler系统为例，我们证明了在明确参数范围内存在混沌吸引子，并验证了导致拓扑熵增长的一系列分岔过程的存在性。所有证明均通过计算机辅助完成。