# Calendar

Mathematical Physics Seminar

## Almost surely recurrent motions in the Euclidean space

Location:  Hill 705
Date & time: Thursday, 29 September 2016 at 2:00PM - 2:11PM

Markus Kunze , University of Cologne :We will show that measure-preserving transformations of$$\R^n$$ are recurrent if they satisfy a certain growth condition depending on the dimension $$n$$. Moreover, it is also shown that this condition is sharp. Examples will include non-autonomous Hamiltonian systems $$\dot{z}=J abla_z H(t, z)$$ of one degree of freedom and $$T$$-periodic in $$t$$, for which our result will imply the existence of a periodic solution, provided that $$abla_z H(t, z) ={\cal O}(|z|^{-\alpha})$$ as $$|z| o\infty$$ for some $$\alpha>1$$ uniformly in $$t$$.

This is joint work with Rafael Ortega (Granada).

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