### Minimal periods in Lipschitz ODEs and Schäffer's girth

Analysis and Geometry Seminar

1st February 2024, 3:30 pm – 4:30 pm

Fry Building, 2.04

In 1969, Yorke showed that any periodic orbit of a Lipschitz ODE in R^{n} must have period at least 2 pi/L, where L is the Lipschitz constant of the right-hand side, and this is sharp. The same result holds in any Hilbert space.

However, if we instead consider the problem in a general Banach space (or even in R^{n} with a different norm), the picture is far less clear.

I will outline what is currently known, and potential links with the notion of the "girth" of a Banach space - the length of the shortest curve in the unit ball joining opposite points - introduced by Schäffer in 1973.

This is joint work with Alejandro Vidal López (XJTLU)

## Comments are closed.