Decay of correlations for normally hyperbolic trapping
Decay of correlations for normally hyperbolic trapping
复制标题
正常双曲线捕获的相关性衰减
DOI：
10.1007/s00222-014-0527-y
复制
发表时间：
2013
影响因子：
3.1
通讯作者：
M. Zworski
中科院分区：
文献类型：
--
作者：
S. Nonnenmacher;M. Zworski
我们证明，对于相空间中通常双曲陷阱的演化问题，相关性随时间呈指数衰减。通常，双曲俘获意味着俘获集是光滑且辛的，并且在与其垂直的方向上的流动是双曲线的。具有这种结构的流包括接触阿诺索夫流、分子动力学中的经典流以及黑洞度量的零测地线流。相关性的衰减是格林函数（截止解）存在无共振带以及半经典参数中这些函数增长的多项式界限的结果。
We prove that for evolution problems with normally hyperbolic trapping in phase space, correlations decay exponentially in time. Normally hyperbolic trapping means that the trapped set is smooth and symplectic and that the flow is hyperbolic in directions transversal to it. Flows with this structure include contact Anosov flows, classical flows in molecular dynamics, and null geodesic flows for black holes metrics. The decay of correlations is a consequence of the existence of resonance free strips for Green’s functions (cut-off resolvents) and polynomial bounds on the growth of those functions in the semiclassical parameter.