Related papers: Cyclicity, hypercyclicity and randomness in self-s…
We introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful in order to study…
In this paper we provide a full characterization of cyclic composition operators defined on the d-dimensional Fock space $\mathcal F(\mathbb C^d)$ in terms of their symbol. Also, we study the supercyclicity and convex-cyclicity of this type…
In this paper we survey a new criteria for solvability of finite groups in terms of number of supersolvable (also known as polycyclic) and non-supersolvable subgroups. In particular, we present original examples of supersolvable groups such…
We prove the following: For any $\rho\in\left(0,1\right)$, if a finite group $G$ has an automorphism with a cycle of length at least $\rho\cdot|G|$, then the index of the solvable radical $\operatorname{Rad}(G)$ in $G$ is bounded from above…
This work investigates the combinatorial structures underlying cyclic conditional freeness and introduces cumulants that serve to linearize the cyclic conditional additive convolution. In the process, we establish the notion of "cyclic…
On a cyclic group of prime order, the non-trivial Dirichlet characters together with their Fourier transforms have constant modulus outside 0 and vanish at 0. Answering a question of H. Cohn, we construct new functions with these…
We prove that in various natural models of a random quotient of a group, depending on a density parameter, for each hyperbolic group there is some critical density under which a random quotient is still hyperbolic with high probability,…
We initiate the study of profinite groups of non-negative deficiency. The principal focus of the paper is to show that the existence of a finitely generated normal subgroup of infinite index in a profinite group $G$ of non-negative…
We give a definition of weakly sofic groups (w-sofic groups). Our definition is rather natural extension of the definition of sofic groups where instead of Hamming metric on symmetric groups we use general bi-invariant metrics on finite…
For a profinite group, we construct a model structure on profinite spaces and profinite spectra with a continuous action. This yields descent spectral sequences for the homotopy groups of homotopy fixed point space and for stable homotopy…
We characterise the profinite Grothendieck-Teichm\"uller group $\widehat{\mathsf{GT}}$ as the group of automorphisms of the profinite completion of a cyclic operad of parenthesised ribbon braids. This operad generates a symmetric monoidal…
The cyclic sieving phenomenon is a well-studied occurrence in combinatorics appearing when a cyclic group acts on a finite set. In this paper, we demonstrate a natural extension of this theory to finite abelian groups. We also present a…
We study different conditions which turn out to be equivalent to equicontinuity for a transitive compact Hausdorff flow with a general group action. Among them are a notion of "regional" equicontinuity, also known as "Furstenberg"…
The article deals with profinite groups in which centralizers are virtually procyclic. Suppose that G is a profinite group such that the centralizer of every nontrivial element is virtually torsion-free while the centralizer of every…
It is known that a group shift on a polycyclic group is necessarily of finite type. We show that, for trivial reasons, if a group does not satisfy the maximal condition on subgroups, then it admits non-SFT abelian group shifts. In…
We discuss selected topics of current research interest in the theory of dynamical systems, with emphasis on dimension theory, multifractal analysis, and quantitative recurrence. The topics include the quantitative versus the qualitative…
We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…
The first aim of this paper is to introduce a class of Markov chains on $\mathbb{Z}_+$ which are discrete self-similar in the sense that their semigroups satisfy an invariance property expressed in terms of a discrete random dilation…
We say that two free probability-measure-preserving actions of countable groups are Shannon orbit equivalent if there is an orbit equivalence between them whose associated cocycle partitions have finite Shannon entropy. We show that if the…
We consider group-valued cocycles over a partially hyperbolic diffeomorphism which is accessible volume-preserving and center bunched. We study cocycles with values in the group of invertible continuous linear operators on a Banach space.…