English

Orthogonal powers and M\"obius conjecture for smooth time changes of horocycle flows

Dynamical Systems 2018-11-13 v1

Abstract

We derive, from the work of M. Ratner on joinings of time-changes of horocycle flows and from the result of the authors on its cohomology, the property of orthogonality of powers for non-trivial smooth time-changes of horocycle flows on compact quotients. Such a property is known to imply P. Sarnak's M\"obius orthogonality conjecture, already known for horocycle flows by the work of J. Bourgain, P. Sarnak and T. Ziegler.

Keywords

Cite

@article{arxiv.1811.04652,
  title  = {Orthogonal powers and M\"obius conjecture for smooth time changes of horocycle flows},
  author = {Livio Flaminio and Giovanni Forni},
  journal= {arXiv preprint arXiv:1811.04652},
  year   = {2018}
}