On the spectrum of anosov diffeomorphisms
On the spectrum of anosov diffeomorphisms
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关于阿诺索夫微分同胚的谱
DOI：
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发表时间：
1980
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影响因子：
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通讯作者：
M. Brin
中科院分区：
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作者：
M. Brin
任何阿诺索夫微分同胚都会在连续矢量场的巴纳赫空间中引入线性算子，该频谱包含在与单位圆不相交的两个环中。主要定理指出，如果这些环足够“窄”，则 f 具有不动点。还证明，iff 作用于下流形（例如环面），则对应于 tof 的代数自同构的谱环总是比 forf 更“窄”。
Any Anosov diffeomorphismf induces a linear operator in the Banach space of continuous vector fields, which spectrum is contained in two annuli both being disjoint with the unit circle. The main theorem states that, if these annuli are sufficiently “narrow”, thenf has a fixed point. It is also proved that, iff acts on an infranilmanifold (e.g., on a torus), then the spectrum annuli for the algebraic automorphism corresponding tof are always more “narrow” than forf.