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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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Department of Mathematics

Department of Mathematics
Rutgers University
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