Sharkovsky Ordering on the Mandelbrot Set

Explore the intricacies of Sharkovsky ordering as applied to the Mandelbrot set in this 31-minute conference talk delivered by Reila Zheng from the University of Toronto. Recorded at the Big Ideas in Dynamics in Geometry: A Hybrid Conference held at UIC on September 29th, 2024, delve into the fascinating intersection of dynamical systems and fractal geometry. Gain insights into how Sharkovsky's theorem, typically associated with one-dimensional dynamics, can be extended to the complex plane through the lens of the iconic Mandelbrot set. Discover new perspectives on the relationship between periodic orbits and the structure of this famous fractal, potentially unveiling novel connections between discrete and continuous dynamical systems.