ترغب بنشر مسار تعليمي؟ اضغط هنا

Livsic theorem for diffeomorphism cocycles

88   0   0.0 ( 0 )
 نشر من قبل Alejandro Kocsard
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We prove the so called Livv{s}ic theorem for cocycles taking values in the group of $C^{1+beta}-diffeomorphisms of any closed manifold of arbitrary dimension. Since no localization hypothesis is assumed, this result is completely global in the space of cocycles and thus extends the previous result of the second author and Potrie [KP16] to higher dimensions.



قيم البحث

اقرأ أيضاً

We prove a Livv{s}ic-type theorem for Holder continuous and matrix-valued cocycles over non-uniformly hyperbolic systems. More precisely, we prove that whenever $(f,mu)$ is a non-uniformly hyperbolic system and $A:M to GL(d,mathbb{R}) $ is an $alpha$ -H{o}lder continuous map satisfying $ A(f^{n-1}(p))ldots A(p)=text{Id}$ for every $pin text{Fix}(f^n)$ and $nin mathbb{N}$, there exists a measurable map $P:Mto GL(d,mathbb{R})$ satisfying $A(x)=P(f(x))P(x)^{-1}$ for $mu$-almost every $xin M$. Moreover, we prove that whenever the measure $mu$ has local product structure the transfer map $P$ is $alpha$-H{o}lder continuous in sets with arbitrary large measure.
159 - Alex Eskin , Carlos Matheus 2013
Let $G$ be a semisimple Lie group acting on a space $X$, let $mu$ be a compactly supported measure on $G$, and let $A$ be a strongly irreducible linear cocycle over the action of $G$. We then have a random walk on $X$, and let $T$ be the associated s hift map. We show that the cocycle $A$ over the action of $T$ is conjugate to a block conformal cocycle. This statement is used in the recent paper by Eskin-Mirzakhani on the classifications of invariant measures for the SL(2,R) action on moduli space. The ingredients of the proof are essentially contained in the papers of Guivarch and Raugi and also Goldsheid and Margulis.
178 - Xiaochun Rong , Xuchao Yao 2020
The $pi_2$-diffeomorphism finiteness result (cite{FR1,2}, cite{PT}) asserts that the diffeomorphic types of compact $n$-manifolds $M$ with vanishing first and second homotopy groups can be bounded above in terms of $n$, and upper bounds on the absolu te value of sectional curvature and diameter of $M$. In this paper, we will generalize this $pi_2$-diffeomorphism finiteness by removing the condition that $pi_1(M)=0$ and asserting the diffeomorphism finiteness on the Riemannian universal cover of $M$.
Given a finite set of quasi-periodic cocycles the random product of them is defined as the random composition according to some probability measure. We prove that the set of $C^r$, $0leq r leq infty$ (or analytic) $k+1$-tuples of quasi periodic coc ycles taking values in $SL_2(mathbb{R})$ such that the random product of them has positive Lyapunov exponent contains a $C^0$ open and $C^r$ dense subset which is formed by $C^0$ continuity point of the Lyapunov exponent For $k+1$-tuples of quasi periodic cocycles taking values in $GL_d(mathbb{R})$ for $d>2$, we prove that if one of them is diagonal, then there exists a $C^r$ dense set of such $k+1$-tuples which has simples Lyapunov spectrum and are $C^0$ continuity point of the Lyapunov exponent.
59 - Mauricio Poletti 2017
We prove that in an open and dense set, Symplectic linear cocycles over time one maps of Anosov flows, have positive Lyapunov exponents for SRB measures.
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