37 citations · 45 across the 7 of their papers we have counts for
8 papers
Symplectic groupoid multiplication and Poisson integrators
Alejandro Cabrera, David Iglesias Ponte, Juan Carlos Marrero
In this paper, we study the role of local symplectic groupoid multiplication in the construction of approximation methods for Hamiltonian flows on the underlying Poisson manifold.…
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…
Unimodularity and invariant volume forms for Hamiltonian dynamics on coisotropic Poisson homogeneous spaces
Ivan Gutierrez-Sagredo, David Iglesias Ponte, Juan Carlos Marrero +1
In this paper, we introduce the notion of a multiplicative unimodularity for a coisotropic Poisson homogeneous space. Then, we discuss the unimodularity and the multiplicative unim…
Almost-Poisson brackets for nonholonomic systems with gyroscopic terms and Hamiltonisation
L. C. García-Naranjo, J. C. Marrero, D. Martín de Diego +1
We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term…
Kirillov structures and reduction of Hamiltonian systems by scaling and standard symmetries
A. Bravetti, S. Grillo, J. C. Marrero +1
In this paper, we discuss the reduction of symplectic Hamiltonian systems by scaling and standard symmetries which commute. We prove that such a reduction process produces a so-cal…
Unimodularity and invariant volume forms for Hamiltonian dynamics on Poisson-Lie groups
I. Gutierrez-Sagredo, D. Iglesias Ponte, J. C. Marrero +2
In this paper, we discuss several relations between the existence of invariant volume forms for Hamiltonian systems on Poisson-Lie groups and the unimodularity of the Poisson-Lie s…
Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
Alessandro Bravetti, Manuel de León, Juan Carlos Marrero +1
We prove that, under some natural conditions, Hamiltonian systems on a contact manifold can be split into a Reeb dynamics on an open subset of and a Liouville dynamics on a…
Discrete dynamics in implicit form
D. Iglesias, J. C. Marrero, D. Martin de Diego +1
A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an applicat…