Almost surely recurrent motions in the Euclidean space

@inproceedings{Kunze2017AlmostSR,
  title={Almost surely recurrent motions in the Euclidean space},
  author={Markus Kunze and Rafael Ortega},
  year={2017}
}
We will show that measure-preserving transformations of Rn are recurrent if they satisfy a certain growth condition depending on the dimension n. Moreover, it is also shown that this condition is sharp. 

References

SHOWING 1-3 OF 3 REFERENCES

A symplectic fixed point theorem on open manifolds

In 1968 Bourgin proved that every measure-preserving, orientationpreserving homeomorphism of the open disk has a fixed point, and he asked whether such a result held in higher dimensions. Asimov, in

Lectures on Bouncing Balls, lecture notes for a course in Murcia, 2013; available at http://www2.math.umd.edu/∼dolgop/BBNotes.pdf

  • 2013

Homeomorphisms of two-dimensional manifolds

  • Houston J. Math. 11,
  • 1985