Related papers: On the normal cycles of subanalytic sets

This paper investigates the exact number of limit cycles given by the averaging theory of first order for the piecewise smooth integrable non-Hamiltonian system \begin{eqnarray*} (\dot{x},\ \dot{y})=\begin{cases} (-y(x+a)^2+\varepsilon…

The usage of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. First we introduce all the necessary concepts of logic, then we prove classical theorems using elementary…

We study analytic and Borel subsets defined similarily to the old example of analytic complete set given by Luzin. Luzin's example, which is essentially a subset of the Baire space, is based on the natural partial order on naturals, i.e.…

We prove that for $1<c<4/3$ the subsequence of the Thue--Morse sequence $\mathbf t$ indexed by $\lfloor n^c\rfloor$ defines a normal sequence, that is, each finite sequence $(\varepsilon_0,\ldots,\varepsilon_{T-1})\in \{0,1\}^T$ occurs as a…

A simple example is used to show that renormalization group limit cycles of effective quantum theories can be studied in a new way. The method is based on the similarity renormalization group procedure for Hamiltonians. The example contains…

This article is written for the Proceedings of the Conference on Current Developments in Mathematics in Harvard University, November 16-17, 2007. It is an exposition of the analytic proof of the finite generation of the canonical ring for a…

Poincar\'e recurrence theorem implies the density of recurrent points for volume-preserving dynamical systems on compact domains. The density of closed orbits in the non-wandering set is one of the essential properties of Axiom A and chaos.…

These notes constitute a survey on the geometric properties of globally subanalytic sets. We start with their definition and some fundamental results such as Gabrielov's Complement Theorem or existence of cell decompositions. We then give…

We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the $C^1$-topology then it…

We use the ultrafilter-convergence axiomatics for topological spaces to motivate in detail a gentle categorical introduction, first to Barr's Set-based relational T-algebras, and then to Burroni's T-preorders internal to a category C, here…

Let $X$ be a real analytic orbifold. Then each stratum of $X$ is a subanalytic subset of $X$. We show that $X$ has a unique subanalytic triangulation compatible with the strata of $X$. We also show that every ${\rm C}^r$-orbifold, $1\leq…

Given the germ of an analytic function on affine space with a smooth critical locus, we prove that the constancy of the stalk cohomology of the Milnor fiber in lowest degree off a codimension two subset of the critical locus implies that…

A proof of the following theorem is given, answering an open problem attributed to Kunen: suppose that $T$ is compact and that $Y$ is the image of $X$ under a perfect map, $X$ is normal, and $Y\times T$ is normal. Then $X \times T$ is…

We give a new proof of the compactness of minimizing sequences of the Sobolev inequalities in the critical case. Our approach relies on a simplified version of the concentration-compactness principle, which does not require any refinement…

Bott and Samuelson constructed explicit cycles representing a basis of the Z_2-homology of the orbits of variationally complete representations of compact Lie groups. As a consequence, all those orbits are taut. We were able to show that an…

A subset $A$ of $\mathbb{N}$ is called an IP-set if $A$ contains all finite sums of distinct terms of some infinite sequence $(x_n)_{n\in \mathbb{N}} $ of natural numbers. Central sets, first introduced by Furstenberg using notions from…

We study two-dimensional subshifts whose horizontal trace (a.k.a. projective subdynamics) contains only points of finite support. Our main result is a classification result for such subshifts satisfying a minimality property. As…

A central result here is the computation of the entire cyclic homology of canonical smooth subalgebras of stable continuous trace C*-algebras having smooth manifolds M as their spectrum. More precisely, the entire cyclic homology is shown…

Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…

Working in the soft-element (classical) viewpoint, we introduce \emph{soft bitopological groups}: soft groups endowed with two soft topologies such that the induced topologies on the set of soft elements make the soft-element group into a…