The classical and quantum features of Nambu mechanics are analyzed and fundamental
issues are resolved. The classical theory is reviewed and developed utilizing varied …

We introduce the concept of natural Poisson bivectors, which generalizes the Benenti
approach to construction of natural integrable systems on Riemannian manifolds and allows …

In this paper, we present neural networks learning mechanical systems that are both
symplectic (for instance particle mechanics) and non-symplectic (for instance rotating rigid …

We study Hamiltonian structures of dynamical systems with three degrees of freedom which
are known for their chaotic properties, namely Lü, modified Lü, Chen, T and Qi systems. We …

A general algebraic condition for the functional independence of 2n-1 constants of motion of
an n-dimensional maximal superintegrable Hamiltonian system has been proved for an …

We first consider the Hamiltonian formulation of n= 3 systems, in general, and show that all
dynamical systems in R 3 are locally bi-Hamiltonian. An algorithm is introduced to obtain …

We study the emergence of oscillatory self-sustained behavior in a nonequilibrium Nambu
system that features an exchange between different kinetical and potential energy forms. To …

In this paper we further investigate some applications of Nambu mechanics in hydro-
dynamical systems. Using the Euler equations for a rotating rigid body Névir and Blender [J …

The dynamics of even topological open membranes relies on Nambu brackets.
Consequently, such 2p-branes can be quantized through the consistent quantization of the …

A new family of skew-symmetric solutions of the Jacobi partial differential equations for finite-
dimensional Poisson systems is characterized and analyzed. Such family has some …