6 papers
Visible Measures along and Distribution of Horocycle Orbits
Adam Kanigowski, Kaitlyn Loyd
Let denote the number of prime factors of , counted with multiplicities. We study the set of weak- limits of the sequence $\frac{1}{N}\sum_{n\leq N}δ_{T^{Ω…
Weak mixing for area preserving flows on surfaces
Adam Kanigowski, Alexey Okunev, Rigoberto Zelada
Let be an area-preserving smooth flow on a compact, connected, orientable surface with at least one but finitely many fixed points. Assume that is an…
Density of orbits of horocycle flows at sub-quadratic polynomial times
Adam Kanigowski, Maksym RadziwiÅÅ
Let be such that the space is not compact. Let be the horocycle flow acting on . We show that for every…
The influence of the maximal summand on ergodic sums of non-integrable observables over rotations
Adam Kanigowski, Tanja I. Schindler
For being an irrational rotation of angle on the one torus and , we compare the behavior of the Birkhoff sum $S_N(Ï)=\sum…
Singularity of the spectrum of typical minimal smooth area-preserving flows in any genus
Krzysztof FrÄ czek, Krzysztof Frączek, Adam Kanigowski +1
We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces, and show that almost every such locally…
Multiple mixing for parabolic systems
Adam Kanigowski, Davide Ravotti
The famous Rokhlin Problem asks whether mixing implies higher order mixing. So far, all the known examples of zero entropy, mixing dynamical systems enjoy a variant of the mixing v…