14 citations · 45 across the 11 of their papers we have counts for
13 papers · 1 filter
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…
Recurrence for smooth curves in the moduli space and application to the billiard flow on nibbled ellipses
Krzysztof Frączek
In view of classical results of Masur and Veech almost every element in the moduli space of compact translation surfaces is recurrent. In this paper we focus on the problem of recu…
Approximate orthogonality of powers for ergodic affine unipotent diffeomorphisms on nilmanifolds
Livio Flaminio, Krzysztof Frączek, Joanna Kułaga-Przymus +1
Let be a connected, simply connected nilpotent Lie group and a lattice. We prove that each ergodic diffeomorphism on the nilmanifold , where $…
Genericity on curves and applications: pseudo-integrable billiards, Eaton lenses and gap distributions
Krzysztof Frączek, Ronggang Shi, Corinna Ulcigrai
In this paper we prove results on Birkhoff and Oseledets genericity along certain curves in the space of affine lattices and in moduli spaces of translation surfaces. We also prove…
On special flows over IETs that are not isomorphic to their inverses
Przemysław Berk, Krzysztof Frączek
In this paper we give a criterion for a special flow to be not isomorphic to its inverse which is a refine of a result in \cite{Fr-Ku-Le}. We apply this criterion to special flows…
On Hausdorff dimension of the set of closed orbits for a cylindrical transformation
Krzysztof Fraczek, Mariusz Lemanczyk
We deal with Besicovitch's problem of existence of discrete orbits for transitive cylindrical transformations where is an irrational rotatio…
Ratner's property and mixing for special flows over two-dimensional rotations
K. Fraczek, M. Lemanczyk
We consider special flows over two-dimensional rotations by on $\T^2$ and under piecewise roof functions satisfying von Neumann's condition $\int_{\T^2}f_x(x,y)\,…
A note on quasi-similarity of Koopman operators
Krzysztof Fraczek, Mariusz Lemanczyk
Answering a question of A. Vershik we construct two non-weakly isomorphic ergodic automorphisms for which the associated unitary (Koopman) representations are Markov quasi-similar.…