Asymptotic flag of an orientable measured foliation
Asymptotic flag of an orientable measured foliation
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可定向测量叶状结构的渐近标志
DOI：
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发表时间：
1993
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通讯作者：
A. Zorich
中科院分区：
文献类型：
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作者：
A. Zorich
本文对一般区间交换变换的Rauzy归纳法中涉及的变换算子的渐近谱性质作了几点说明。对这些猜想取模，我们得到了表面上一般可定向测量叶理的叶子动力学的非常精确的近似。主要的对象，这是我们得到的是一个标志的第一（上）同调群的表面1 g，其中g是一个亏格的表面。子空间的这一标志推广了渐近圈，特别是最小子空间被渐近圈所张成。假设这个子空间的标志提供了一个新的不变量，即叶理。我们通过一个特殊的例子来说明这些结果，这个例子来自于I.Dinnikov提出的费米面上的电子动力学模型。虽然我们不能提供任何严格的数学证明的声明，作者相信他们的有效性是由许多计算机实验的有力支持。得到了肯定的结果。
We state several conjectures on asymptotic "spectral properties" of transformation operators involved in Rauzy induction for a generic interval exchange transformation. Modulo these conjectures we get a very précise approximation for dynamics of leaves of a generic orientable measured foliation on a surface. The main object, which we get is a flag of subspaces in the first (co)homology group of the surface of dimensions 1 g, where g is a genus of the surface. Tins flag of subspaces generalizes asymtotic cycle; in particular the smal lest subspace is spanned by the asymtotic cycle. Presumably this flag of subspaces provides a new invariant, of foliation. We illustrate the conjectures by treating a spécifie example, which cornes from a model of électron dynamics on a Fermi-surface suggested by I.Dinnikov. Though we can not provide any strict mat hem ati cal proofs of the conjectures proclaimed, authors belief in their validity is strongly supported by numerous computer expeiïments. which gave affirmative results.