1999/07/22 by M. Wilkinson, Wilkinson, M., B. Mehlig +1
Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Quantum chaos and dynamical systems #chao-dyn #nlin.CD
paper · pdf · doi:10.48550/arxiv.chao-dyn/9907031
4 pages, RevTeX, 3 Postscipt figures
arxiv created 1999/07/22 · openalex publication_date 1999/07/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It might be anticipated that there is statistical universality in the long-time classical dynamics of chaotic systems, corresponding to the universal correspondence of their quantum spectral statistics with random matrix models. We argue that no such universality exists. We discuss various statistical properties of long period orbits: the distribution of the phase-space density of periodic orbits of fixed length and a correlation function of periodic-orbit actions, corresponding to the universal quantum spectral two-point correlation function. We show that bifurcations are a mechanism for correlations of periodic-orbit actions. They lead to a result which is non-universal, and which in general may not be an analytic function of the action difference.