不完全状態同定と力学系の頑健性

概要

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We introduce the concept of generative pointer, which is an extended subobject classifier with local identity (i.e. an incomplete indication or identification). Generative pointer is derived from a generalization of the emergence process of rational numbers. It metamorphoses hierarchical structure in dynamical systems into heterarchical one. Generally, intermittency arises as a critical state on a dynamical system. Thus it is sensitive with respect to parameter shifts. In contrast, on-off intermittency is ubiquitously observed for a wide range of parameter values when a generative pointer is applied to a Henon map system. This fact implies robustness of the criticality against parameter shifts. The concept of structural stability or trajectory stability of dynamical systems is based on the specific invariable map, but robustness, in contrast with stability, is based on the dynamic change of the map. Thus, in our view, the robustness does not conflict with the emergence but coincides with it.
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