Amanda Hampton, Department of Applied Mathematics, University of Colorado Boulder

What is Anti-integrability?

Anti-integrability is a relatively new concept used to study the development and destruction of chaos in discrete dynamical systems. Often, problems in dynamics are posed as a perturbation from regularity: how much can one perturb a regular, non-chaotic system until it becomes chaotic? Anti-integrability allows us to take the ‘opposite’ approach by posing the problem as a perturbation from chaos towards regularity and uses tools like the Contraction Mapping Theorem, the Implicit Function Theorem, and symbolic dynamics. In this talk, we will discuss this technique, its context, the needed tools, and a couple of examples in an accessible and approachable manner. With some equations, but mostly pictures and cartoons, we’ll learn what anti-integrability really is and where exactly it fits into the study of dynamical systems.