# MATH3201 Dynamical Systems and Chaos

MATH3201 is a Mathematics Level III course. See the course overview below.

Units of credit: 6

Prerequisites: 12 units of credit in Level II Mathematics courses including MATH2120 or MATH2130 or MATH2121 or MATH2221, and MATH2501 or MATH2601.

Cycle of offering: Term 2

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH3201, you can log into UNSW Moodle of this course.

#### Course Overview

Many nonlinear ODEs do not have explicit solutions. The dynamical systems approach shifts the focus from finding explicit solutions to discovering geometric properties of solutions. It also recognises that even a small amount of nonlinearity in a physical system can be responsible for very complicated chaotic behaviour.

In this course you will learn the fundamentals of dynamical systems in (continuous time) nonlinear ODEs and in (discrete time) nonlinear maps, allowing you to analyse the local and global behaviour of nonlinear systems.

Nonlinear maps: The building blocks of dynamics

Fixed points, periodic points, invariant sets, recurrence, nonwandering sets, symbolic dynamics, conjugacy, sensitive dependence on initial conditions, Lyapunov exponents, fractals, Stable Manifold Theorem, chaotic attractors, Smale's Horseshoe, ergodic theory.

Nonlinear ODEs: A geometric, qualitative approach to ODEs

Phase portraits, fixed points, periodic and chaotic trajectories, sources, sinks, and saddles, stable and unstable subspaces, robustness, hyperbolicity, stability, conjugacy, stable and unstable manifolds, bifurcations.