10 citations · 18 across the 11 of their papers we have counts for
11 papers
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…
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 notion of foul…
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…
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…
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…
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…
Canonical transformations: from the coordinate based approach to the geometric one
R. Azuaje, A. M. Escobar-Ruiz
In this paper the theory of time-dependent and time-independent canonical transformations is considered from a geometric perspective. Both the geometric formalism and the coordinat…
Scaling symmetries and canonoid transformations in Hamiltonian systems
R. Azuaje, A. Bravetti
We investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic,…
On particular integrability in classical mechanics
A. M. Escobar-Ruiz, R. Azuaje
In this study the notion of particular integrability in Classical Mechanics, introduced in [J. Phys. A: Math. Theor. 46 025203, 2013], is revisited within the formalism of symplect…
Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems
R. Azuaje
In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamilt…
Canonical and canonoid transformations for Hamiltonian systems on (co)symplectic and (co)contact manifolds
R. Azuaje, A. M. Escobar-Ruiz
In this paper we present canonical and canonoid transformations considered as global geometrical objects for Hamiltonian systems. Under the mathematical formalisms of symplectic, c…