Stability of statistical properties in two-dimensional piecewise hyperbolic maps
Stability of statistical properties in two-dimensional piecewise hyperbolic maps
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DOI：
10.1090/s0002-9947-08-04464-4
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发表时间：
2008-01-01
影响因子：
1.3
通讯作者：
Liverani, Carlangelo
中科院分区：
文献类型：
--
作者：
Demers, Mark F.;Liverani, Carlangelo
通过直接研究转移算子在适当的分布空间上的作用，我们研究了分段光滑动力系统的统计性质。我们完成了这样一个程序的情况下，二维地图的一致有界的二阶导数。对于手头的系统类，我们得到一个完整的描述SRB措施，他们的统计特性和他们的稳定性，相对于许多类型的扰动，包括确定性和随机扰动和孔。
We investigate the statistical properties of a piecewise smooth dynamical system by directly studying the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional maps with uniformly bounded second derivative. For the class of systems at hand, we obtain a complete description of the SRB measures, their statistical properties and their stability with respect to many types of perturbations, including deterministic and random perturbations and holes.