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 Rn 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 Rn 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)
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