Nilfactors of Rm-actions and configurations in sets of positive upper density in Rm
Tamar Ziegler
Abstract
We use ergodic theoretic tools to solve a classical problem in geometric Ramsey theory. Let E be a measurable subset of Rm, with positive upper density. Let V=0,v1,...,vk be a subset of Rm. We show that for r large enough, we can find an isometric copy of rV arbitrarily close to E. This is a generalization of a theorem of Furstenberg, Katznelson and Weiss showing a similar property for m=k=2.
Create a lesson
Related papers
ω-limit sets of triangular maps over periodic orbits of the base
Juan Luis García Guirao
The full Kolakoski shift is topologically transitive
Andrew C. Mitchell, James J. Walton, Michael F. Whittaker
Delay-induced multirhythmicity in a 3-cell inhibitory network
Xinxin Qie, Morten Gram Pedersen, Jian Song et al.
Natural Expansiveness and Equilibrium States for Semiflows
Nelda Tamblay, Juan Francisco Peña
Largest-Angle Bisection and Statistical Regularization of Triangle Shapes
Jérôme Michaud
Planar Central Configurations of Four Equal Masses: Classification and Morse Indices
Xiaoxiang Huangfu, Huatong Shen