Related papers: An Oka Principle for a Parametric Infinite Transit…

We consider the discrete Couzin-Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools. In this article, we propose a kinetic (mean-field) version of the CVA model and provide its…

A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…

We prove that in a compact manifold of dimension $n\geq 2$, a $C^{1+\alpha}$ volume-preserving diffeomorphisms that are robustly transitive in the $C^1$-topology have a dominated splitting. Also we prove that for 3-dimensional compact…

We prove that the openness of the set of maps, between a Stein manifold and an Oka manifold, transverse to a stratification of a complex analytic subvariety in the target implies that the stratification is Whitney $a$-regular. Our result…

This paper deals with the analytic continuation of holomorphic automorphic forms on a Lie group $G$. We prove that for any discrete subgroup $\Gamma$ of $G$ there always exists a non-trivial holomorphic automorphic form, i.e., there exists…

For every $r\in\mathbb{N}_{\geq 2}\cup\{\infty\}$, we prove a $C^r$-orbit connecting lemma for dynamically coherent and plaque expansive partially hyperbolic diffeomorphisms with 1-dimensional orientation preserving center bundle. To be…

Local action principles on a manifold $\M$ are invariant (if at all) only under diffeomorphisms that preserve the boundary of $\M$. Suppose, however, that we wish to study only part of a system described by such a principle; namely, the…

We prove that for any infinite-type orientable surface S there exists a collection of essential curves {\Gamma} in S such that any homeomorphism that preserves the isotopy classes of the elements of {\Gamma} is isotopic to the identity. The…

Let S be an arbitrary real surface, with or without boundary, contained in a hypersurface M of the complex euclidean space \C^2, with S and M of class C^{2, a}, where 0 < a < 1. If M is globally minimal, if S is totally real except at…

Most transport theorems---that is, a formula for the rate of change of an integral in which both the integrand and domain of integration depend on time---involve domains that evolve according to a flow map. Such domains are said to be…

We hope to see how much for a model M of some completion T of PA (Peano Arithmetic) does M restriction {<} determine M, say up to isomorphism. We advance in characterizing for non-standard models M of PA the "minimal" set {(a,b):n < a < b…

We study holomorphic self-maps of non-ordered n-point configuration spaces C^n(X), where X is either affine or projective complex line. The complex Lie group Aut(X) acts diagonally on C^n(X). We prove that for n>4 every endomorphism F of…

For a smooth manifold of any dimension greater than one, we present an open set of smooth endomorphisms such that any of them has a transitive attractor with a non-empty interior. These maps are $m$-fold non-branched coverings, $m \ge 3$.…

In this work we develop a new criterion for the existence of topological horseshoes for surface homeomorphisms in the isotopy class of the identity. Based on our previous work on forcing theory, this new criterion is purely topological and…

Let $X$ be a compact metric space. By $2^X$ we denote the hyperspace of all closed and non-empty subsets of $X$ endowed with the Hausdorff metric. Let $f:X\to X$ be a continuous function. In this paper we study some topological properties…

An old theorem of Weil and Kodaira says that for a compact K\"ahler manifold $X$ there is a closed logarithmic $1$-form with residue divisor $D$ if and only if $D$ is homologous to zero in $H_{2n-2}(X,\mathbb C)$. In the first part of this…

Equations of motion of large N quantum mechanics are solved for infinite N in the case of unbroken global O(N) symmetry. It is shown that the only correction to the action is a change in the potential. All characteristics of the motion…

We provide a complete classification of when the homeomorphism group of a stable surface, $\Sigma$, has the automatic continuity property: Any homomorphism from Homeo$(\Sigma)$ to a separable group is necessarily continuous. This result…

A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…

Let $(X,d,f)$ be a topological dynamical system, where $(X,d)$ is a compact metric space and $f:X\to X$ is a continuous map. We define $n$-ordered empirical measure of $x\in X$ by \begin{align*}…