Renato Vitolo, Mark P. Holland, and Christopher A.T. Ferro
Robust Extremes in Chaotic Deterministic Systems
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ABSTRACT.  A chaotic deterministic system exhibits robust extremes when the statistics of its extreme values depend smoothly on the system's control parameters. Such robustness can be exploited to enhance the precision and accuracy of statistical estimators. It is conjectured here that robust chaos is sufficient for robust extremes. This is demonstrated for 1D Lorenz maps and illustrated numerically for the Lorenz63 model. It is also outlined how these ideas can be applied to more complex chaotic 
systems.