The goal of this paper is proving the existence and then localizing globalfixed points for nilpotent groups generated by homeomorphisms of the planesatisfying a certain Lipschitz condition. The condition is inspired in aclassical result of Bonatti for commuting diffeomorphisms of the 2-sphere andin particular it is satisfied by diffeomorphisms, not necessarily of class$C^{1}$, whose linear part at every point is uniformly close to the identity.In this same setting we prove a version of the Cartwright-Littlewood theorem,obtaining fixed points in any continuum preserved by a nilpotent action.
展开▼
机译：本文的目的是证明存在并定位由满足一定Lipschitz条件的平面同胚性生成的幂等群的全局不动点。该条件是从Bonatti转换2球面的微分同构关系的经典结果中得到启发的，尤其是它由微分同构关系满足，不一定是$ C ^ {1} $类，其在每个点上的线性部分都一致地接近于恒等式。在相同的情况下，我们证明了卡特赖特-利特伍德定理的一个版本，在幂幂所保留的任何连续谱中获得不动点。
展开▼
