arXiv subjects
Publications and source records attributed to Héctor Figueroa.
This is a short review on the Faà di Bruno formulas, and some Hopf algebras associated to them. These allow, among several other things, a short proof of the Lie-Scheffers theorem, and relating the Lagrange inversion formulas with antipodes. The link of Faà di Bruno formulas with the theory of set partitions is developed in some detail.
We consider Feynman-Dyson's proof of Maxwell's equations using the Jacobi identities on the velocity phase space. In this paper we generalize the Feynman-Dyson's scheme by incorporating the non-commutativity between various spatial coordinates along with the velocity coordinates. This allows us to study a generalized class of Hamiltonian systems. We explore various dynamical flows associated to the Souriau form associated to this generalized Feynman-Dyson's scheme. Moreover, using the Souriau form we show that these new classes of generalized systems are volume preserving mechanical systems.
The time evolution operator $K$ is introduced in the graded context and its main properties are discussed. In particular, the operator $K$ is used to analize the projectability of constraint functions arising in the Lagrangian formalism for singular Lagrangians.
Using supervector fields and graded forms along a morphism, we study the geometry of ordinary differential superequations, extend the formalism of higher order Lagrangian mechanics to the graded context and prove a generalization of Noether's theorem.