An alternative approach to the ergodic theory of measured foliations on surfaces
An alternative approach to the ergodic theory of measured foliations on surfaces
复制标题
DOI：
10.1017/s0143385700001383
复制
发表时间：
1981-12
影响因子：
0.9
通讯作者：
M. Rees
中科院分区：
文献类型：
--
作者：
M. Rees
摘要我们考虑测量的表面叶理，和间隔交换。我们给出替代证明下列定理首先证明Masur和（独立）维奇。作用于射影空间的测量叶理（相对于一个自然的'勒贝格'措施）的表面上的同态群是遍历的。几乎所有测量的叶理都是唯一遍历的。几乎所有的区间交换（同样，关于自然的勒贝格测度）都是唯一遍历的。
Abstract We consider measured foliations on surfaces, and interval exchanges. We give alternative proofs of the following theorems first proved by Masur and (independently) Veech. The action of the diffeomorphism group of the surface on the projective space of measured foliations (with respect to a natural ‘Lebesgue’ measure) is ergodic. Almost all measured foliations are uniquely ergodic. Almost all interval exchanges (again, with respect to a natural ‘Lebesgue’ measure) are uniquely ergodic.