Examples of diffeomorphism group cocycles with no periodic approximation
Examples of diffeomorphism group cocycles with no periodic approximation
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没有周期性近似的微分同胚群余循环的示例
DOI：
10.1090/proc/14103
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发表时间：
2017
影响因子：
1
通讯作者：
Sebastián Hurtado
中科院分区：
文献类型：
--
作者：
Sebastián Hurtado
<p>我们构造了一个有限生成的子组
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ml</mml:annotation></mml:semantics></mml:math></inline-formula>:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">S</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:mo> x <！——x——></mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">S</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </</p>mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex"> \operatorname Diff^ {}{\infty (}\mathbb S^3 {}\times\mathbb S^1)</mml:annotation> </ ml:semantics> </mml:math> </inline-formula>其中每个元素都共轭于等距，但使得群作用本身远非等距（群具有“导数的指数增长”）。作为推论，我们得到了一个局部常量<inline-formula content-type="math/mathml"> <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML“ altttext =”上限D i f f上标正常无穷基线左括号双划上限S³乘以双划上限S上标1基线右括号”> <mml:semantics> <mml：打开> <mml:msup> <mml:mi> </mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">∞<！——∞——></mml:mi> </mml:mrow> </mml:msup> <mml:mo> <！-- -- -- -- -- -- -- -- -- -- -- -- - <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">S</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:mo> x <！——x——></mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">S</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex"> {}\operatorname Diff^ {}{\infty (}\mathbb S^3 {}\times\mathbb S^1)</mml:annotation> </ ml:semantics> </mml:math> </inline-公式>值的双曲动力系统上的循环，该系统在其周期轨道上具有椭圆行为，但保留了非零顶光纤-李雅普诺夫指数的测度。此外，我们还提供了不满足周期逼近性质的Banach环的新例子。系统39 (2019),pp. 689-706 .</p>{}
<p>We construct a finitely generated subgroup of <inline-formula content-type="math/mathml">
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<mml:annotation encoding="application/x-tex">\operatorname {Diff}^{\infty }(\mathbb {S}^3 \times \mathbb {S}^1)</mml:annotation>
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</inline-formula> where every element is conjugate to an isometry but such that the group action itself is far from isometric (the group has “exponential growth of derivatives”). As a corollary, one obtains a locally constant <inline-formula content-type="math/mathml">
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</inline-formula> valued cocycle over a hyperbolic dynamical system which has elliptic behavior over its periodic orbits but which preserves a measure with non-zero top fiber-Lyapunov exponent. Additionally, we provide new examples of Banach cocycles not satisfying the periodic approximation property as first shown in Ergodic Theory Dynam. Systems 39 (2019), pp. 689–706.</p>