6 papers
Fouling maps and polynomial first integrals from symmetric tensor fields
Rafael Azuaje, Juan Carlos Marrero, Edith Padrón
Under the framework of time-independent Hamiltonian mechanics on the cotangent bundles of the configuration spaces of mechanical systems, we introduce the concept of fou…
Hamiltonian reduction from particular integrals
R. Azuaje, A. M. Escobar-Ruiz, I. Gutierrez-Sagredo
We develop a geometric reduction mechanism generated by systems of particular integrals, namely, families of functions whose time derivatives close linearly on the family. Their co…
Nonlinear Lissajous orbits and particular superintegrability
A. M. Escobar-Ruiz, R. Azuaje
We investigate the geometry of classical trajectories generated by separable two-dimensional polynomial potentials of the form , wher…
Jacobi-Haantjes manifolds, integrability and dissipative mechanical systems
Rafael Azuaje, Piergiulio Tempesta
The notion of Jacobi-Haantjes manifold, consisting of a Jacobi manifold endowed with an algebra of extended Haantjes operator fields, is proposed as a natural geometric framework w…
Canonical and Canonoid transformations for Hamiltonian systems on locally conformal symplectic manifolds
Rafael Azuaje, Xuefeng Zhao
This paper is focused on the development of the notions of canonical and canonoid transformations within the framework of Hamiltonian Mechanics on locally conformal symplectic mani…
Two-dimensional classical superintegrable systems: polynomial algebra of integrals
A. M. Escobar-Ruiz, R. Azuaje, J. C. Gordiano
In this work, we investigate generic classical two-dimensional (2D) superintegrable Hamiltonian systems H, characterized by the existence of three functionally independent integral…