Coarse-Grained Structure of a Physical (Strange) Attractor. Analytical Solution
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Publication:5477074
zbMATH Open1095.37010arXivcond-mat/0309026MaRDI QIDQ5477074
Publication date: 20 July 2006
Abstract: The structure of the physical and strange attractors is inherently associated with the boundedness of fluctuations. The idea behind the boundedness is that a stable long-term evolution of any natural and engineered system is possible if and only if the fluctuations that the system exerts are bounded so that the system permanently stays within its thresholds of stability. It has been established that the asymptotic structure of the physical and strange attractors is identical. Now it is found out that though the non-asymptotic behavior is universal it can be very different, namely: on coarse-graining the physical attractors can exhibit a variety of behavior while the strange attractors always have hyperuniversal properties. Yet, under certain levels of coarse-graining both physical and strange attractors match non-asymptotically a variety of noise type behavior.
Full work available at URL: https://arxiv.org/abs/cond-mat/0309026
Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Attractors of solutions to ordinary differential equations (34D45)
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