ترغب بنشر مسار تعليمي؟ اضغط هنا

There is no minimal action of Z^2 on the plane

60   0   0.0 ( 0 )
 نشر من قبل Frederic Le Roux
 تاريخ النشر 2010
  مجال البحث
والبحث باللغة English
 تأليف Frederic Le Roux




اسأل ChatGPT حول البحث

In this paper it is proved that there is no minimal action (i.e. every orbit is dense) of Z^2 on the plane. The proof uses the non-existence of minimal homeomorphisms on the infinite annulus (Le Calvez-Yoccozs theorem), and the theory of Brouwer homeomorphisms.

قيم البحث

اقرأ أيضاً

76 - Saurya Das 2020
We show that if Dark Matter is made up of light bosons, they form a Bose-Einstein condensate in the early Universe. This in turn naturally induces a Dark Energy of approximately equal density and exerting negative pressure.This explains the so-called coincidence problem.
46 - J. P. Boronski , Alex Clark , 2016
The following well known open problem is answered in the negative: Given two compact spaces $X$ and $Y$ that admit minimal homeomorphisms, must the Cartesian product $Xtimes Y$ admit a minimal homeomorphism as well? A key element of our construction is an inverse limit approach inspired by combination of a technique of Aarts & Oversteegen and the construction of Slovak spaces by Downarowicz & Snoha & Tywoniuk. This approach allows us also to prove the following result. Let $phicolon Mtimesmathbb{R}to M$ be a continuous, aperiodic minimal flow on the compact, finite--dimensional metric space $M$. Then there is a generic choice of parameters $cinmathbb{R}$, such that the homeomorphism $h(x)=phi(x,c)$ admits a noninvertible minimal map $fcolon Mto M$ as an almost 1-1 extension.
Numerous recent works show that overparameterization implicitly reduces variance for min-norm interpolators and max-margin classifiers. These findings suggest that ridge regularization has vanishing benefits in high dimensions. We challenge this narr ative by showing that, even in the absence of noise, avoiding interpolation through ridge regularization can significantly improve generalization. We prove this phenomenon for the robust risk of both linear regression and classification and hence provide the first theoretical result on robust overfitting.
We prove some ergodic-theoretic rigidity properties of the action of SL(2,R) on moduli space. In particular, we show that any ergodic measure invariant under the action of the upper triangular subgroup of SL(2,R) is supported on an invariant affine s ubmanifold. The main theorems are inspired by the results of several authors on unipotent flows on homogeneous spaces, and in particular by Ratners seminal work.
148 - Song Shao , Xiangdong Ye 2016
It is shown that any non-PI minimal system is Li-Yorke sensitive. Consequently, any minimal system with nontrivial weakly mixing factor (such a system is non-PI) is Li-Yorke sensitive, which answers affirmatively an open question by Akin and Kolyada.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا