Kirillov structures and reduction of Hamiltonian systems by scaling and standard symmetries

• Autores: Bravetti, A.; Grillo, Sergio Daniel; Marrero, J. C.; Padrón, E.
• Año de publicación: 2024
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Scaling symmetries; Kirillov structures; Hamiltonian systems; Contact structures
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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-called Kirillov Hamiltonian system. Moreover, we show that if we reduce first by the scaling symmetries and then by the standard ones or in the opposite order, we obtain equivalent Kirillov Hamiltonian systems. In the particular case when the configuration space of the symplectic Hamiltonian system is a Lie group , which coincides with the symmetry group, the reduced structure is an interesting Kirillov version of the Lie–Poisson structure on the dual space of the Lie algebra of . We also discuss a reconstructionprocess for symplectic Hamiltonian systems which admit a scaling symmetry. All the previous results are illustrated in detail with some interesting examples.
Fil: Bravetti, A.. Universidad Nacional Autónoma de México; México
Fil: Grillo, Sergio Daniel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Fil: Marrero, J. C.. Universidad de La Laguna; España
Fil: Padrón, E.. Universidad de La Laguna; España