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Mechanical presymplectic structures and Marsden-Weinstein reduction of time-dependent Hamiltonian systems

Autor: Gutierrez-Sagredo, I., Ponte, D. Iglesias, Marrero, J. C., Padrón, E.

In 1986, Albert proposed a Marsden-Weinstein reduction process for cosymplectic structures. In this paper, we present the limitations of this theory in the application of the reduction of symmetric time-dependent Hamiltonian systems. As a consequence

Externí odkaz: http://arxiv.org/abs/2411.11997

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Unimodularity and invariant volume forms for Hamiltonian dynamics on Poisson-Lie groups

Autor: Gutierrez-Sagredo, I., Ponte, D. Iglesias, Marrero, J. C., Padrón, E., Ravanpak, Z.

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 structure. In particular, we prove that Hamiltonian vector fields on a

Externí odkaz: http://arxiv.org/abs/2207.05511

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Mechanical Hamiltonian systems with respect to linear Poisson structures and Jacobi-Reeb dynamics

Autor: Ponte, D. Iglesias, Marrero, J. C., Padrón, E.

In this paper, we present a relation between Jacobi-Reeb dynamics and the dynamics associated with a mechanical Hamiltonian system with respect to a linear Poisson structure on a vector bundle. For this purpose, we will use the so-called Jacobi bundl

Externí odkaz: http://arxiv.org/abs/2204.13523

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Poly-Poisson structures

Autor: Iglesias-Ponte, D., Marrero, J. C., Vaquero, M.

In this paper we introduce poly-Poisson structures as a higher-order extension of Poisson structures. It is shown that any poly-Poisson structure is endowed with a polysymplectic foliation. It is also proved that if a Lie group acts polysymplecticall

Externí odkaz: http://arxiv.org/abs/1209.4003

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Locally conformal symplectic groupoids

Autor: Iglesias-Ponte, D., Marrero, J. C.

Locally conformal symplectic (l.c.s.) groupoids are introduced as a generalization of symplectic groupoids. We obtain some examples and we prove that l.c.s. groupoids are examples of Jacobi groupoids in the sense of \cite{IM}. Finally, we describe th

Externí odkaz: http://arxiv.org/abs/math/0301108

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