Abstract:
Linear flows on a finite-dimensional normed space X constitute what
is arguably the simplest class of dynamical systems. When exactly are
two such flows equivalent, that is, when do they have the same orbits,
up to a homeomorphism h of X? The answer, unsurprisingly, depends
on the smoothness of h, which in turn gives rise to several natural
classifications of linear flows up to equivalence. Some classification
theorems date back to the 1970s and have been part of linear systems
folklore ever since. While these results are easy to intuit for familiar
forms of smoothness (say, if h is bi-Lipschitz or differentiable), their
proofs tend to involve some delicate and potentially murky analysis.
This talk presents several new tools that facilitate an elementary
approach to the classification of linear flows. (Joint work with A. Wynne.)