Related papers: A note on pseudofinite dimension and forking
This paper is divided into two parts. The first part concerns several standard scenarios for how short-range spin glasses might behave at low temperature. Earlier theorems of the authors are reviewed, and some new results presented,…
This paper provides asymptotic structure at spatial infinity of plane steady Stokes flow in exterior domains when the obstacle is rotating with constant angular velocity. The result shows that there is no longer Stokes paradox due to the…
A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal…
In this paper, we introduce discrete conics, polygonal analogues of conics. We show that discrete conics satisfy a number of nice properties analogous to those of conics, and arise naturally from several constructions, including the…
We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that…
We examine the conditions for appearance of symmetry breaking bifurcation in damped and periodically driven pendulum in the case of strong damping. We show that symmetry breaking, unlike other nonlinear phenomena, can exist at high…
In this talk we use nonlinear realizations to study the spontaneous partial breaking of rigid and local supersymmetry.
This paper summarizes substantive new results derived by a student team (the first three authors) under the direction of the fourth author at the 2005 session of the KSU REU ``Brainstorming and Barnstorming''. The main results are a…
For a Euclidean building $X$ of type $A_{2}$, we classify the 0-dimensional subbuildings $A$ of $\partial_{T}X$ that occur as the asymptotic boundary of closed convex subsets. In particular, we show that triviality of the holonomy of a…
We provide an example of a non-finitely generated group which admits a nonempty strongly aperiodic SFT. Furthermore, we completely characterize the groups with this property in terms of their finitely generated subgroups and the roots of…
In this article we study how a subshift can simulate another one, where the notion of simulation is given by operations on subshifts inspired by the dynamical systems theory (factor, projective subaction...). There exists a correspondence…
We discuss some examples in which symplectic monodromy (provably or conjecturally) splits off the symplectic mapping class group, hoping to illustrate different techniques and inputs to the arguments. Along the way we formulate several open…
A new, extended nonlinear framework of the ordinary real analysis incorporating a novel concept of {\em duality structure} and its applications into various nonlinear dynamical problems is presented. The duality structure is an asymptotic…
We give a characterization for asymptotic dimension growth. We apply it to CAT(0) cube complexes of finite dimension, giving an alternative proof of N. Wright's result on their finite asymptotic dimension. We also apply our new…
We explicitly construct several Poisson structures with compact support. For example, we show that any Poisson structure on $\R^n$ with polynomial coefficients of degree at most two can be modified outside an open ball, such that it becomes…
A subset of the finite dimensional hypercube is said to be equilateral if the distance of any two distinct points equals a fixed value. The equilateral dimension of the hypercube is defined as the maximal size of its equilateral subsets. We…
This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. An explicit and essentially unique decomposition of such…
We study asymptotics of various Euclidean geometric phenomena as the dimension tend to infinity.
We present constructions of countable two-dimensional subshifts of finite type (SFTs) with interesting properties. Our main focus is on properties of the topological derivatives and subpattern posets of these objects. We present a countable…
We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1.