Analytic-non-integrability of an integrable analytic Hamiltonian system

About Analytic Non Integrability

We discuss non existence of analytic first integrals for analytic diffeomorphisms possessing a hyperbolic fixed point with a homoclinic connection.

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...

Analytic Non-integrability of the Suslov Problem

In this work we consider the Suslov problem, which consists of a rotation motion of a rigid body, whose center of mass is located at one axis of inertia, around a fixed point O in a constant gravity field restricted to a nonholonomic constraint. The integrability and non-integrability has been established by a number of authors for the nongeneric values of b = (b1, b2, b3) which is the unit vec...

On the analytic integrability of the cored galactic Hamiltonian

We provide a complete characterization of the analytic first integrals of the cored galactic Hamiltonian.

Arnold diffusion in perturbations of analytic integrable Hamiltonian systems