Robust minimality of strong foliations for DA diffeomorphisms: -volume expansion and new examples
Robust minimality of strong foliations for DA diffeomorphisms: -volume expansion and new examples
复制标题
DA微分同胚的强叶状结构的鲁棒极小性：-体积膨胀和新例子
DOI：
10.1090/tran/8590
复制
发表时间：
2022
影响因子：
1.3
通讯作者：
Jiagang Yang
中科院分区：
文献类型：
--
作者：
Jana Rodriguez Hertz;Raúl Ures;Jiagang Yang
Let . f. f. be a . C. 2. C^2. partially hyperbolic diffeomorphisms of . T. 3. mathbb {T}^3. (not necessarily volume preserving or transitive) isotopic to a linear Anosov diffeomorphism . A. A. with eigenvalues . λ. s. >. 1. >. λ. c. >. λ. u. .. begin{equation} lambda _{s}>1>lambda _{c}>lambda _{u}. end{equation}. Under the assumption that the set . {. x. :. ∣. log. . det. (. T. f. ∣. E. c. u. (. x. ). ). ∣≤. log. . λ. u. }. begin{equation} {x: ,mid log det (Tfmid _{E^{cu}(x)})mid leq log lambda _{u} } end{equation}. has zero volume inside any unstable leaf of . f. f. where . E. c. u. =. E. c. ⊕. E. u. E^{cu} = E^coplus E^u. is the center unstable bundle, we prove that the stable foliation of . f. f. is . C. 1. C^1. robustly minimal, i.e., the stable foliation of any diffeomorphism . C. 1. C^1. sufficiently close to . f. f. is minimal. In particular, . f. f. is robustly transitive..We build, with this criterion, a new example of a . C. 1. C^1. open set of partially hyperbolic diffeomorphisms, for which the strong stable foliation and the strong unstable foliation are both minimal.
Let . f. f. be a . C. 2. C^2. partially hyperbolic diffeomorphisms of . T. 3. mathbb {T}^3. (not necessarily volume preserving or transitive) isotopic to a linear Anosov diffeomorphism . A. A. with eigenvalues . λ. s. >. 1. >. λ. c. >. λ. u. .. begin{equation} lambda _{s}>1>lambda _{c}>lambda _{u}. end{equation}. Under the assumption that the set . {. x. :. ∣. log. . det. (. T. f. ∣. E. c. u. (. x. ). ). ∣≤. log. . λ. u. }. begin{equation} {x: ,mid log det (Tfmid _{E^{cu}(x)})mid leq log lambda _{u} } end{equation}. has zero volume inside any unstable leaf of . f. f. where . E. c. u. =. E. c. ⊕. E. u. E^{cu} = E^coplus E^u. is the center unstable bundle, we prove that the stable foliation of . f. f. is . C. 1. C^1. robustly minimal, i.e., the stable foliation of any diffeomorphism . C. 1. C^1. sufficiently close to . f. f. is minimal. In particular, . f. f. is robustly transitive..We build, with this criterion, a new example of a . C. 1. C^1. open set of partially hyperbolic diffeomorphisms, for which the strong stable foliation and the strong unstable foliation are both minimal.