当前位置: X-MOL 学术J. Am. Math. Soc. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Lebesgue spectrum of countable multiplicity for conservative flows on the torus
Journal of the American Mathematical Society ( IF 3.9 ) Pub Date : 2021-03-25 , DOI: 10.1090/jams/970
Bassam Fayad , Giovanni Forni , Adam Kanigowski

Abstract:We study the spectral measures of conservative mixing flows on the $2$-torus having one degenerate singularity. We show that, for a sufficiently strong singularity, the spectrum of these flows is typically Lebesgue with infinite multiplicity. For this, we use two main ingredients: (1) a proof of absolute continuity of the maximal spectral type for this class of non-uniformly stretching flows that have an irregular decay of correlations, (2) a geometric criterion that yields infinite Lebesgue multiplicity of the spectrum and that is well adapted to rapidly mixing flows.


中文翻译:

环面上保守流的可数重数勒贝格谱

摘要:我们研究了具有一个退化奇点的 $2$-环面上的保守混合流的谱测度。我们表明,对于足够强的奇点,这些流的频谱通常是具有无限多重性的勒贝格。为此,我们使用两个主要成分:(1)证明此类具有不规则相关性衰减的非均匀拉伸流的最大光谱类型的绝对连续性,(2)产生无限勒贝格多重性的几何标准的频谱,并且非常适合快速混合流动。
更新日期:2021-03-25
down
wechat
bug