Related papers: Approximately transitive dynamical systems and sim…

A topological group is (openly) almost-elliptic if it contains a(n open) dense subset of elements generating relatively-compact cyclic subgroups. We classify the (openly) almost-elliptic connected locally compact groups as precisely those…

We show that a topological dynamical system is either minimal or have positive topological entropy. Moreover, for equicontinuous systems, we show that topological transitivity, minimality and orbit gluing property are equivalent. These…

We will answer a question raised by Emmanuel Dror Farjoun concerning the existence of torsion-free abelian groups G such that for any ordered pair of pure elements there is a unique automorphism mapping the first element onto the second…

We investigate a slight weakening of the classical property of strong approximation, which we call almost strong approximation, for connected reductive algebraic groups over global fields with respect to special sets of valuations. While…

Suppose a residually finite group $G$ acts cocompactly on a contractible complex with strict fundamental domain $Q$, where the stabilizers are either trivial or have normal $\mathbb{Z}$-subgroups. Let $\partial Q$ be the subcomplex of $Q$…

A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…

A hovel is a generalization of the Bruhat-Tits building that is associated to an almost split Kac-Moody group G over a non-Archimedean local field. In particular, G acts strongly transitively on its corresponding hovel $\Delta$ as well as…

In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties…

We constract various subgroups of the group of isometries of universal Urysohn spaces (unique complete separable metric space which is iniversal and homogeneous) including abelian groups which act transitively, and free groups which are…

Quasi-particles described by Green's functions of equilibrium systems exhibit non-Hermitian topological phenomena because of their finite lifetime. This non-Hermitian perspective on equilibrium systems provides new insights into correlated…

We prove that every transitive and non minimal semigroup with dense minimal points is sensitive. When the system is almost open, we obtain a generalization of this result.

We consider linear groups which do not contain unipotent elements of infinite order, which includes all linear groups in positive characteristic, and show that this class of groups has good properties which resemble those held by groups of…

We give a complete characterization of abelian subgroups of GL(n, R) with a locally dense (resp. dense) orbit in R^n. For finitely generated subgroups, this characterization is explicit and it is used to show that no abelian subgroup of…

We define for discrete finitely presented groups a new property related to their asymptotic representations. Namely we say that a groups has the property AGA if every almost representation generates an asymptotic representation. We give…

We introduce a relaxation of stability, called almost sure stability, which is insensitive to perturbations by subsets of Loeb measure $0$ in a non-standard finite group. We show that almost sure stability satisfies a stationarity principle…

We construct smooth actions of arbitrary compact Lie groups on complex projective spaces, such that the corresponding transformations arising from the group action do not preserve any symplectic structure on the complex projective space.

Building on earlier results for regular maps and for orientably regular chiral maps, we classify the non-abelian finite simple groups arising as automorphism groups of maps in each of the 14 Graver-Watkins classes of edge-transitive maps.

We characterize simple complex abelian varieties and simple abelian surfaces in terms of primitivity of translation automorphisms. Applying this together with a result due to Diller and Favre, we then classify all primitive birational…

Let $E$ be a subset of positive integers such that $E\cap\{1,2\}\ne\emptyset$. A weakly mixing finite measure preserving flow $T=(T_t)_{t\in\Bbb R}$ is constructed such that the set of spectral multiplicities (of the corresponding Koopman…

I discuss particular solutions of the integrable systems, starting from well-known dispersionless KdV and Toda hierarchies, which define in most straightforward way the generating functions for the Gromov-Witten classes in terms of the…