Adam Kanigowski

activity

20132026

most citedPrime orbits for some smooth flows on

T^{2}

69 citations · 158 across the 38 of their papers we have counts for

collaborators

48 papers

math.DS2026

IC-rigidity for abelian actions

Adam Kanigowski, Kosma Kasprzak, Miriam Lorenzo-Laguno

Let $G$ be a group acting continuously on a compact metric space $X$ . This naturally induces an action of $G$ on the space $K (X)$ of nonempty compact subsets of $X$ . In […

math.DS2026

Visible Measures along $Ω (n)$ and Distribution of Horocycle Orbits

Adam Kanigowski, Kaitlyn Loyd

Let $Ω (n)$ denote the number of prime factors of $n$ , counted with multiplicities. We study the set $A c c^{Ω} (x)$ of weak- $^{*}$ limits of the sequence $\frac{1}{N}\sum_{n\leq N}δ_{T^{Ω…

math.DS2026

Weak mixing for area preserving flows on surfaces

Adam Kanigowski, Alexey Okunev, Rigoberto Zelada

Let $(ϕ_{t})$ be an area-preserving smooth flow on a compact, connected, orientable surface $M$ with at least one but finitely many fixed points. Assume that $(ϕ_{t})$ is anal…

math.DS2025

Density of orbits of horocycle flows at sub-quadratic polynomial times

Adam Kanigowski, Maksym Radziwiłł

Let $Γ \subset P S L (2, R)$ be such that the space $X = Γ\ P S L (2, R)$ is not compact. Let $(h_{t})$ be the horocycle flow acting on $X$ . We show that for every $x…

math.DS2025

The influence of the maximal summand on ergodic sums of non-integrable observables over rotations

Adam Kanigowski, Tanja I. Schindler

For $R_{α}$ being an irrational rotation of angle $α$ on the one torus $T$ and $ϕ (x) = \frac{1}{x} - \frac{1}{1 - x}$ , we compare the behavior of the Birkhoff sum $S_N(ϕ)=\sum_{k=…

math.DS2025

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…

math.DS2024

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…

math.DS2024

Horocycle flow at product of two primes

Giovanni Forni, Adam Kanigowski, Maksym Radziwiłł

We show that if $Γ$ is a co-compact arithmetic lattice in $S L (2, R)$ or $Γ = S L (2, Z)$ then the horocycle orbit of every non-periodic point $x \in S L (2, R) /Γ$ …

math.DS2023

On the local Fourier uniformity problem for small sets

Adam Kanigowski, Mariusz Lemańczyk, Florian Karl Richter +1

We consider vanishing properties of exponential sums of the Liouville function $λ$ of the form $$ \lim_{H\to\infty}\limsup_{X\to\infty}\frac{1}{\log X}\sum_{m\leq X}\frac{1}{m}\sup…

math.DS2023

A non-mixing Arnold flow on a surface

Bassam Fayad, Adam Kanigowski, Rigoberto Zelada

We construct a smooth area preserving flow on a genus 2 surface with exactly one open uniquely ergodic component, that is asymmetrically bounded by separatrices of non-degenerate s…

math.DS2023

Limit theorems for low dimensional generalized $(T, T^{- 1})$ transformations

Dmitry Dolgopyat, Changguang Dong, Adam Kanigowski +1

We consider generalized $(T, T^{- 1})$ transformations such that the base map satisfies a multiple mixing local limit theorem and anticoncentration large deviation bounds and in the…

math.DS2022

Smooth zero entropy flows satisfying the classical central limit theorem

Dmitry Dolgopyat, Bassam Fayad, Adam Kanigowski

We construct conservative analytic flows of zero metric entropy which satisfy the classical central limit theorem.

math.DS2021

Counterexamples to a rigidity conjecture

Giovanni Forni, Adam Kanigowski

We discuss several counterexamples to a rigidity conjecture of K. Khanin, which states that under some quantitative condition on non-existence of periodic orbits, $C^{0}$ conjugacy i…

math.DS2021★ 4 cited

Exponential mixing implies Bernoulli

Dmitry Dolgopyat, Adam Kanigowski, Federico Rodriguez-Hertz

Let $f$ be a $C^{1 + α}$ diffeomorphism of a compact manifold $M$ preserving a smooth measure $μ$ . We show that if $f : (M, μ) \to (M, μ)$ is exponentially mixing then it is Bernoulli.

math.DS2021

On arithmetic functions orthogonal to deterministic sequences

Adam Kanigowski, Joanna Kulaga-Przymus, Mariusz Lemańczyk +1

We prove Veech's conjecture on the equivalence of Sarnak's conjecture on Möbius orthogonality with a Kolmogorov type property of Furstenberg systems of the M\''obius function. This…

math.DS2020

Flexibility of statistical properties for smooth systems satisfying the central limit theorem

Dmitry Dolgopyat, Changguang Dong, Adam Kanigowski +1

In this paper we exhibit new classes of smooth systems which satisfy the Central Limit Theorem (CLT) and have (at least) one of the following properties: (1) zero entropy; (2) weak…

math.DS2020★ 69 cited

Prime orbits for some smooth flows on $T^{2}$

Adam Kanigowski

We consider a class of smooth mixing flows $T^{α, γ}$ on $T^{2}$ with one degenerated fixed point $x_{0} \in T^{2}$ of power type $γ \in (- 1, 0)$ . We prove that for a $G_{δ}$ …

math.DS2020★ 2 cited

Slow entropy of higher rank abelian unipotent actions

Adam Kanigowski, Philipp Kunde, Kurt Vinhage +1

We study slow entropy invariants for abelian unipotent actions $U$ on any finite volume homogeneous space $G /Γ$ . For every such action we show that the topological slow entropy can…

math.DS2020★ 8 cited

Survey on entropy-type invariants of sub-exponential growth in dynamical systems

Adam Kanigowski, Anatole Katok, Daren Wei

Measure-theoretic and topological entropy are classical invariants in the theory of dynamical systems. There are several recently developed entropy type invariants for systems of s…

math.DS2020★ 1 cited

Prime number theorem for analytic skew products

Adam Kanigowski, Mariusz Lemańczyk, Maksym Radziwiłł

We establish a prime number theorem for all uniquely ergodic, analytic skew products on the $2$ -torus $T^{2}$ . More precisely, for every irrational $α$ and every $1$ -periodi…

math.DS2020★ 4 cited

Prime number theorem for regular Toeplitz subshifts

Krzysztof Frączek, Adam Kanigowski, Mariusz Lemańczyk

We prove that neither a prime nor {an l-almost prime} number theorem hold in the class of regular Toeplitz subshifts. But, {when a quantitative strengthening of the regularity with…

math.DS2020

Mixing properties of generalized $T, T^{- 1}$ transformations

Dmitry Dolgopyat, Changguang Dong, Adam Kanigowski +1

We study mixing properties of generalized $T, T^{- 1}$ transformation. We discuss two mixing mechanisms. In the case the fiber dynamics is mixing, it is sufficient that the driving…

math.DS2019★ 1 cited

Bernoulli property for certain skew products over hyperbolic systems

Changguang Dong, Adam Kanigowski

We study the Bernoulli property for a class of partially hyperbolic systems arising from skew products. More precisely, we consider a hyperbolic map $(T, M, μ)$ , where $μ$ is a Gibbs…

math.DS2019★ 9 cited

Singularity of the spectrum for smooth area-preserving flows in genus two and translation surfaces well approximated by cylinders

Jon Chaika, 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, when the genus of the surf…

IC-rigidity for abelian actions

Visible Measures along Ω(n) and Distribution of Horocycle Orbits

Weak mixing for area preserving flows on surfaces

Density of orbits of horocycle flows at sub-quadratic polynomial times

The influence of the maximal summand on ergodic sums of non-integrable observables over rotations

Singularity of the spectrum of typical minimal smooth area-preserving flows in any genus

Multiple mixing for parabolic systems

Horocycle flow at product of two primes

On the local Fourier uniformity problem for small sets

A non-mixing Arnold flow on a surface

Limit theorems for low dimensional generalized (T,T−1) transformations

Smooth zero entropy flows satisfying the classical central limit theorem

Counterexamples to a rigidity conjecture

Exponential mixing implies Bernoulli

On arithmetic functions orthogonal to deterministic sequences

Flexibility of statistical properties for smooth systems satisfying the central limit theorem

Prime orbits for some smooth flows on T2

Slow entropy of higher rank abelian unipotent actions

Survey on entropy-type invariants of sub-exponential growth in dynamical systems

Prime number theorem for analytic skew products

Prime number theorem for regular Toeplitz subshifts

Mixing properties of generalized T,T−1 transformations

Bernoulli property for certain skew products over hyperbolic systems

Singularity of the spectrum for smooth area-preserving flows in genus two and translation surfaces well approximated by cylinders

Visible Measures along $Ω (n)$ and Distribution of Horocycle Orbits

Limit theorems for low dimensional generalized $(T, T^{- 1})$ transformations

Prime orbits for some smooth flows on $T^{2}$

Mixing properties of generalized $T, T^{- 1}$ transformations