Agnes Scott College

Focus on Math

**Title**:

Rigorous computation for chaotic systems

**Abstract**:

A dynamical system is one that evolves over time according to fixed rules — for example, the motion of the planets, the populations of competing species of animals, or the formation of traffic jams. Simple rules can often lead to chaotic behavior. It’s natural to try to use computers to understand these systems, but unfortunately even the tiniest numerical error renders the results useless for pure mathematics, which demands exact answers, not approximations. The problems are especially bad when we try to study the long-term behavior of chaotic dynamical systems, since small errors can quickly accumulate into big ones. We’ll look at these problems, and at ways in which we can overcome them to use numerical approximation to prove mathematically rigorous results.