Related papers: Approximation in ergodic theory, Borel, and Cantor…
Two conjectures about homology groups, K-groups and topological full groups of minimal etale groupoids on Cantor sets are formulated. We verify these conjectures for many examples of etale groupoids including products of etale groupoids…
`Shape dynamics' is meant here in the sense of a type of conformogeometrical reformulation of GR, some of which have of late been considered as generalizations of or alternatives to GR. This note concerns in particular cases based on the…
Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This…
This paper is an overview of my recent work on abstract homomorphisms of algebraic groups. It is based on a talk given at the Conference on Group Actions and Applications in Geometry, Topology, and Analysis held in Kunming in July 2012.
The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…
This is a survey about certain "almost homomorphisms" and "almost linear" functionals (called quasi-morphisms and quasi-states) in symplectic topology and their applications to Hamiltonian dynamics, functional-theoretic properties of…
We study mean ergodicity in amenable operator semigroups and establish the connection to the convergence of strong and weak ergodic nets. We then use these results in order to show the convergence of uniform families of ergodic nets that…
In this paper, we first prove the variational principle for amenable packing topological pressure. Then we obtain an inequality concerning amenable packing pressure for factor maps. Finally, we show that the equality about packing…
In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems, when we consider ergodic optimization restricted on the…
Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…
Relationships between a chaotic behavior and closely related properties of topological transitivity, sensitivity to initial conditions, density of closed orbits of homeomorphism groups and their countable products are investigated. We…
We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…
In this article we give the basic concept of the "Topological Numbers" in theory of quasiperiodic functions. The main attention is paid to apperance of such values in transport phenomena including Galvanomagnetic phenomena in normal metals…
Carrier graphs of groups representing subgroups of a given relatively hyperbolic groups are introduced and a combination theorem for relatively quasi-convex subgroups is proven. Subsequently a theory of folds for such carrier graphs is…
We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…
Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…
Using methods from algebraic topology and group cohomology, I pursue Grothendieck's question on equality of geometric and cohomological Brauer groups in the context of complex-analytic spaces. The main result is that equality holds under…
Motivated by Sarnak's conjecture on M\"obius orthogonality, we investigate the general problem of orthogonality for a bounded sequence to topological models of characteristic classes of measure-preserving automorphisms. Our main observation…
This is a survey article describing some recent results at the interface of homogeneous dynamics and Diophantine approximation.
In this paper we formulate three problems concerning topological properties of sets generating Borel non-sigma-compact groups. In case of the concrete F_\sigma\delta-subgroup of the Cantor group this gives an equivalent reformulation of the…