12 citations · 14 across the 6 of their papers we have counts for
8 papers
Singularity of the spectrum of typical minimal smooth area-preserving flows in any genus
Krzysztof Frączek, Adam Kanigowski, Corinna Ulcigrai
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…
On the ergodicity of anti-symmetric skew products with singularities and its applications
Przemysław Berk, Krzysztof Frączek, Frank Trujillo
We introduce a novel method for proving ergodicity for skew products of interval exchange transformations (IETs) with piecewise smooth cocycles having singularities at the ends of…
On resonant energy sets for Hamiltonian systems with reflections
Krzysztof Frączek
We study two uncoupled oscillators, one horizontal and one vertical, moving in a rectilinear polygon (with only vertical and horizontal sides) and undergoing elastic reflections at…
Solving the cohomological equation for locally hamiltonian flows, part II -- global obstructions
Krzysztof Frączek, Minsung Kim
Continuing the research initiated in \cite{Fr-Ki2}, we study the existence of solutions and their regularity for the cohomological equations for locally Hamiltonian flows (…
Solving the cohomological equation for locally hamiltonian flows, part I -- local obstructions
Krzysztof Frączek, Minsung Kim
We study the cohomological equation for smooth locally Hamiltonian flows on compact surfaces. The main novelty of the proposed approach is that it is used to study the regul…
New phenomena in deviation of Birkhoff integrals for locally Hamiltonian flows
Krzysztof Frączek, Minsung Kim
We consider smooth locally Hamiltonian flows on compact surfaces of genus to prove their deviation of Birkhoff integrals for smooth observables. Our work generalizes resu…