2021-03-04

UTAPwiki/セミナー/宇宙物理学セミナー

Speaker: Toshinori Hayashi

Tittle: Dynamical system and chaos

Abstract:
The dynamical system consists of simultaneous ordinary differential equations,
and appears in many fields including Physics, Biology, etc.
In this talk, I will present the basics of the dynamical system, and show how we can
understand the dynamics from a geometrical point of view.
First, I will introduce the dynamical system in one-dimensional space, and show some features in the system.
Although the one-dimensional system is extremely simple, it still provides some important
viewpoints including bifurcation mechanisms.
Second, I will move on to the two-dimensional system, and do a brief review on some important behaviors,
including the index theory, and the Poincaré-Bendixson theorem.
The latter theorem is important since it efficiently restricts the allowed motions in two-dimensional plane systems.
Finally, I briefly mention the dynamics in higher dimensional systems, and touch on chaotic behaviors appeared there.