Colloquia — Summer 2012

Friday, June 29, 2012

Abstract

Suppose that \((X,d)\) is a finite-dimensional metric space, and \(f\) is a homeomorphism from \(X\) onto itself. Such a situation arises, for example, when \(X\) is the finite-dimensional attractor of some infinite-dimensional dynamical systems. I will discuss the problem of embedding \(X\) into a finite-dimensional Euclidean space \(R^n\) so that it is the attractor of some iterated homeomorphism \(F\) from \(R^n\) onto itself. The problem is still not completely solved, but the partial resolution I will present is bound up in an interesting way with topological properties of attractors of homeomorphisms. This is joint work with Jaime Sanchez-Gabites (Ciudad Real).