2020/04/29 by A. Latifi, Latifi, Anouchah, Vasileios Basios +3
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2004.14336
openalex publication_date 2020/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we show that "Labyrinth walks", the conservative version of "Labyrinth chaos" and member of the Thomas-Rössler 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!