Scaling symmetries, contact reduction and Poincaré’s dream

• Verfasst von: Bravetti, Alessandro [VerfasserIn]
• Verfasst von: Jackman, Connor [VerfasserIn]
• Verfasst von: Sloan, David [VerfasserIn]
• Titel: Scaling symmetries, contact reduction and Poincaré’s dream
• Verf.angabe: Alessandro Bravetti, Connor Jackman, David Sloan
• E-Jahr: 2023
• Jahr: 9 October 2023
• Umfang: 43 S.
• Fussnoten: Gesehen am 24.09.2024
• Titel Quelle: Enthalten in: Journal of physics. A, Mathematical and theoretical
• Ort Quelle: Bristol : IOP Publ., 2007
• Jahr Quelle: 2023
• Band/Heft Quelle: 56(2023), 43, Artikel-ID 435203, Seite 1-43
• ISSN Quelle: 1751-8121
• DOI: doi:10.1088/1751-8121/acfddd
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1903358329

Abstract

We state conditions under which a symplectic Hamiltonian system admitting a certain type of symmetry (a scaling symmetry) may be reduced to a type of contact Hamiltonian system, on a space of one less dimension. We observe that such contact reductions underly the well-known McGehee blow-up process from classical mechanics. As a consequence of this broader perspective, we associate a type of variational Herglotz principle associated to these classical blow-ups. Moreover, we consider some more flexible situations for certain Hamiltonian systems depending on parameters, to which the contact reduction may be applied to yield contact Hamiltonian systems along with their Herglotz variational counterparts as the underlying systems of the associated scale-invariant dynamics. From a philosophical perspective, one obtains an equivalent description for the same physical phenomenon, but with fewer inputs needed, thus realizing Poincaré’s dream of a scale-invariant description of the Universe.