Non-integrability of a Weakly Integrable Hamiltonian System

Non–integrability of a Weakly Integrable Hamiltonian System

The geometric approach to mechanics based on the Jacobi metric allows to easily construct natural mechanical systems which are integrable (actually separable) at a fixed value of the energy. The aim of the present paper is to investigate the dynamics of a simple prototype system outside the zero-energy hypersurface. We find that the general situation is that in which integrability is not preser...

An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system

In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =langle I_0, I_1, I_2rangle$, where $I_k(h)=int_{H=h}x^ky,dx$ and $H(x,y)=frac{1}{2}y^2+frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $hin(0,frac{1}{2})$. To this end, we use the criterion and tools developed by...

Hamiltonian formulation and integrability of a complex symmetric nonlinear system

The integrability of a complex generalisation of the ’elegant’ system, proposed by D. Fairlie [1] and its relation to the Nahm equation and the Manakov top is discussed. PACS: 02.30.Ik, 45.20.Jj, 02.30.Hq

Integrability and Level Crossing Manifolds in a Quantum Hamiltonian System

Hamiltonian Structure and Integrability

To describe dynamical systems we usually make suitable approximations in the hope of finding valid descriptions of their characteristic quantities. But even after such approximations we mostly cannot write down explicitly how these quantities depend on time, usually such a dependence is much to complicated to be computed explicitly. Therefore we commonly write down dynamical systems in their in...