Stochastic Stability¶for Contracting Lorenz Maps and Flows
Stochastic Stability¶for Contracting Lorenz Maps and Flows
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收缩洛伦兹图和流的随机稳定性¶
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
R. Metzger
中科院分区：
文献类型：
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作者：
R. Metzger
摘要：在文献[M]中，我们证明了收缩Lorenz-like映射的绝对连续不变测度的存在性，并构造了收缩Lorenz-like映射流的Sinai-Ruelle-Bowen测度.在这里，我们证明了这样的一维映射的随机稳定性，并使用这个结果来证明，相应的流产生这些映射是随机稳定的小扩散型扰动下，即使如Rovella [Ro]所示，他们是持久的，只有在测量理论意义上的参数空间。对于一维映射，我们也证明了Baladi和维亚纳[BV]意义下的强随机稳定性。
Abstract: In a previous work [M], we proved the existence of absolutely continuous invariant measures for contracting Lorenz-like maps, and constructed Sinai–Ruelle–Bowen measures f or the flows that generate them. Here, we prove stochastic stability for such one-dimensional maps and use this result to prove that the corresponding flows generating these maps are stochastically stable under small diffusion-type perturbations, even though, as shown by Rovella [Ro], they are persistent only in a measure theoretical sense in a parameter space. For the one-dimensional maps we also prove strong stochastic stability in the sense of Baladi and Viana[BV].