Os sistemas Hamiltonianos formam uma das classes mais importantes de equações diferenciais. Além de constituírem o formalismo central da física clássica, sua aplicação se estende a uma grande variedade de outros campos de ...

Consider a symplectic manifold M, a Hamiltonian vector field X and a fibration Π:M→N. Related to these data we have a generalized version of the (time-independent) Hamilton–Jacobi equation: the Π-HJE for X, whose unknown ...

In this paper we develop, in a geometric framework, a Hamilton–Jacobi Theory for general dynamical systems. Such a theory contains the classical theory for Hamiltonian systems on a cotangent bundle and recent developments ...

We study some symplectic submanifolds in the cotangent bundle of a factorizable Lie group defined by second class constraints. By applying the Dirac method, we study many issues of these spaces as fundamental Dirac brackets, ...

In this paper we develop a geometric version of the Hamilton-Jacobi equation in the Poisson setting. Specifically, we "geometrize" what is usually called a complete solution of the Hamilton-Jacobi equation. We use some ...

The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulation developed by Chirikov is applied to the NesvornA1/2-Morbidelli analytic model of three-body (three-orbit) ...

The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulation developed by Chirikov is applied to the Nesvorný-Morbidelli analytic model of three-body (three-orbit) ...

In this paper, we study the extended Hamilton–Jacobi Theory in the context of dynamical systems with symmetries. Given an action of a Lie group G on a manifold M and a G-invariant vector field X on M, we construct complete ...