Singular cotangent models in fluids with dissipation
In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a -cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in -cotangent bundles featuring two models: the canonical (or non-twiste...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/384652 |
| Online Access: | https://hdl.handle.net/2117/384652 https://dx.doi.org/10.1016/j.physd.2023.133655 |
| Access Level: | Open access |
| Keyword: | Symplectic manifolds Geometry, Algebraic B-symplectic geometry Fluids with dissipation Manifold with boundary Cotangent models Twisted cotangent models Escape orbits Varietats simplèctiques Geometria algebraica Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Summary: | In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a -cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in -cotangent bundles featuring two models: the canonical (or non-twisted) model and the twisted one. The canonical one models systems on manifolds with boundary and the twisted one represents Hamiltonian systems with a singularity on the fiber. The twisted cotangent model includes (for linear potentials) the case of fluids with dissipation. We prove (non)-existence of cotangent lift dynamics and show the existence of an infinite number of escape orbits in this model. We also discuss more general physical interpretations of the twisted and non-twisted -symplectic models. Twisted -symplectic models yield in a natural way escape orbits that go to the critical set. Under compactness assumptions those escape orbits are continued as singular periodic orbits in the sense of Miranda and Oms (2021) and Miranda (2020). These models offer a Hamiltonian formulation for systems which are dissipative, extending the horizons of Hamiltonian dynamics and opening a new approach to study non-conservative systems. |
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