Dynamical Complexity in the Rössler System

Explore the dynamical complexity of the Rössler system in this 51-minute lecture from the Simons Semester on Dynamics. Delve into the analytical connection between the Rössler equations and the one-dimensional logistic family. Learn how the existence of a specific type of heteroclinic connection at certain parameter values leads to the verification of infinitely many periodic orbits and their topological characterization, without assuming hyperbolicity conditions. Discover how these ideas extend to prove that the return map for the flow in a small parameter neighborhood is at least as complex as the logistic family, using a newly defined sense of complexity.