2019/12/30 by Anouchah Latifi, Latifi, Anouchah, Vasileios Basios +1
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #nlin.CD
paper · pdf · doi:10.48550/arxiv.1912.12780
10 pages,3 figures The publication will be enlarged with new results and the contribution of a new coauthor. Some typos spotted and must be fixed more details have to be added
arxiv created 2020/02/24 · arxiv updated 2020/02/26
We provide here a comprehensive proof that the so-called Labyrinth chaos systems, a member of the Thomas-Rössler (TR) class of systems do not admit a Hamiltonian; yet they admit a vector potential. The proof starts from the general case of TR systems, which are in general non-conservative and we show that this is also true for the conservative (volume-preserving) case known as `Labyrinth chaos'. To our knowledge, this is the first instance reported where a conservative chaotic system does not, in principle, admit a Hamiltonian symplectic structure. Still, a vector potential is readily admissible and thus, constructed.