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arXiv · 2004.14336

Labyrinth walks: An elegant chaotic conservative non-Hamiltonian system

Anouchah Latifi·Vasileios Basios·Chris G. Antonopoulos
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Abstract

In this paper, we show that "Labyrinth walks", the conservative version of "Labyrinth chaos" and member of the Thomas-R\"ossler class of systems, does not admit an autonomous Hamiltonian as a constant function in time, and as a consequence, does not admit a symplectic structure. However, it is conservative, and thus admits a vector potential, being at the same time chaotic. This exceptional set of properties makes "Labyrinth walks" an elegant example of a chaotic, conservative, non-Hamiltonian system, with only unstable stationary points in its phase space, arranged in a 3-dimensional grid. As a consequence, "Labyrinth walks", even though is a deterministic system, it exhibits motion reminiscent of fractional Brownian motion in stochastic systems!

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Anouchah Latifi, Vasileios Basios, Chris G. Antonopoulos. 2020-04-29. Labyrinth walks: An elegant chaotic conservative non-Hamiltonian system. https://arxiv.org/abs/2004.14336

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