Dynamical Systems on Three Manifolds Part I: Knots, Links and Chaos - Nonlinear Sciences > Chaotic DynamicsReport as inadecuate




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Abstract: In this paper, we give an explicit construction of dynamical systems definedwithin a solid torus containing any knot or link and arbitrarily knottedchaos. The first is achieved by expressing the knots in terms of braids,defining a system containing the braids and extending periodically to obtain asystem naturally defined on a torus and which contains the given knottedtrajectories. To get explicit differential equations for dynamical systemscontaining the braids, we will use a certain function to define a tubeneigbourhood of the braid. The second one, generating chaotic systems, isrealized by modeling the Smale horseshoe.



Author: Yi Song, S. P. Banks, David Diaz Dept. of Automatic Control and Systems Engineering, University of Sheffield, UK

Source: https://arxiv.org/



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