The purpose of this article is to show that a C1 differential system on Rn which admits a set
of n− 1 independent C2 conservation laws defined on an open subset Ω⊆ Rn, is essentially …

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 …

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 reduce the problem of constructing bi-Hamiltonian structure in three dimensions to the
solutions of a Riccati equation in moving coordinates of Frenet–Serret frame. All explicitly …

Hamiltonian dynamics are characterized by a function, called the Hamiltonian, and a
Poisson bracket. The Hamiltonian is a conserved quantity due to the anti-symmetry 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 …

In this paper, we describe some relevant dynamical and geometrical properties of the
Rabinovich system from the Poisson geometry and the dynamics point of view. Starting with …

It is well known for physicists that in order to describe dynamical systems of finite number of
degrees of freedom in the macro-and micro-scale, classical and quantum mechanics …

In this paper, we elucidate the key role played by the cosymplectic geometry in the theory of
time dependent Hamiltonian systems in 2 D. We generalize the cosymplectic structures to …

Recently, Kupershmidt [38] presented a Lie algebraic derivation of a new sixth-order wave
equation, which was proposed by Karasu-Kalkani et al.[31]. In this paper, we demonstrate …