Chaotic Dynamical Systems (354-0-81)

Instructors

Aaron W Brown

Meeting Info

Lunt Hall 101: Mon, Wed, Fri 2:00PM - 2:50PM

Overview of class

A dynamical system is any system whose state changes according to some fixed rule. The theory of dynamical systems is relatively young in the long history of mathematical discovery and development. Its origins date to the late 19th century, but a wave of research activity since the 1970s was partially inspired by the computation and visualization abilities of emerging computer technology.

This course will focus on discrete dynamical systems that exhibit chaotic behavior. We will start with the examples of the shift map, the tent map, and the logistic family to introduce the concept of chaos, and explore further properties of chaotic behaviors through Lyapunov exponents, conjugacy, and bifurcations. Additional topics to be covered include fractals, self-similar dimensions, complex dynamics, and an exploration of Julia sets and the Mandelbrot set. We will also make frequent use of computation technology to augment our understanding and inspire our mathematical investigations.

The prerequisite of this course is a course in linear algebra. The course will also assume some familiarity with computer programming, and many of the homework assignments will involve simple programming in Mathematica.

Class Materials (Required)

978-0367235994
A first course in chaotic dynamical systems : theory and experiment, 2nd. Ed
Devaney
CRC Press

Class Materials (Suggested)

No suggested materials. See required materials.

Class Attributes

Formal Studies Distro Area

Enrollment Requirements

Enrollment Requirements: Prerequisite: Students must have completed MATH 240-0 (or equivalent).

Associated Classes

DIS - Lunt Hall 104: Thurs 2:00PM - 2:50PM