Date:
Tue, 19/05/202612:00-13:00
Location:
Manchester Faculty Lounge
Title:
The Mechanics of Chaos in One-Dimensional Continuous Maps
Abstract:
This presentation reviews the 1975 paper "Period Three Implies Chaos" by Tien-Yien Li and James A. Yorke, regarding the emergence of chaotic behavior in one-dimensional continuous maps. The paper proves that the simple existence of a period-three orbit leads to the existence of periodic points of every integer period and the formation of an uncountable "scrambled set" of points. We will discuss the chaotic nature of these trajectories, which neither converge to periodic orbits nor to each other, instead exhibiting infinite oscillations.
The Mechanics of Chaos in One-Dimensional Continuous Maps
Abstract:
This presentation reviews the 1975 paper "Period Three Implies Chaos" by Tien-Yien Li and James A. Yorke, regarding the emergence of chaotic behavior in one-dimensional continuous maps. The paper proves that the simple existence of a period-three orbit leads to the existence of periodic points of every integer period and the formation of an uncountable "scrambled set" of points. We will discuss the chaotic nature of these trajectories, which neither converge to periodic orbits nor to each other, instead exhibiting infinite oscillations.