Labyrinth Chaos is not Hamiltonian but still has a Vector Potential
arXiv:1912.12780
Abstract
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.
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