Brackets in Multicontact Geometry and Multisymplectization
Abstract
Abstract In this paper, we introduce a graded bracket of forms on multicontact manifolds. This bracket satisfies a graded Jacobi identity as well as two different versions of the Leibniz rule, one of them being a weak Leibniz rule, extending the well-known notions in contact geometry. In addition, we develop the multisymplectization of multicontact structures to relate these brackets to the ones present in multisymplectic geometry and obtain the field equations in an abstract context. The Jacobi bracket also permits to study the evolution of observables and study the dissipation phenomena, which we also address. Finally, we apply the results to classical dissipative field theories.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Control and Stability of Dynamical Systems
Geometric and Algebraic Topology
Publication details
- Journal / source
- Mediterranean Journal of Mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 23
- Issue
- 2
- Publication date
- 1 March 2026
- Language
- EN