Zobrazeno 1 - 10
of 107
pro vyhledávání: '"Salnikov, Vladimir"'
Autor:
Chekeres, Olga, Salnikov, Vladimir
Previously, Wilson surface observables were interpreted as a class of Poisson sigma models. We profit from this construction to define and study the super version of Wilson surfaces. We provide some `proof of concept' examples to illustrate modificat
Externí odkaz:
http://arxiv.org/abs/2403.09820
We recall the question of geometric integrators in the context of Poisson geometry, and explain their construction. These Poisson integrators are tested in some mechanical examples. Their properties are illustrated numerically and they are compared t
Externí odkaz:
http://arxiv.org/abs/2303.15883
Following recent results of A.K. and V.S. on $\mathbb Z$-graded manifolds, we give several local and global normal forms results for $Q$-structures on those, i.e. for differential graded manifolds. In particular, we explain in which sense their relev
Externí odkaz:
http://arxiv.org/abs/2212.05579
In this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from ``unlabelled'' ordinary differential equations describing mechanical systems. The algorithm we suggest solves the problem in two phases.
Externí odkaz:
http://arxiv.org/abs/2207.07124
Autor:
Kotov, Alexei, Salnikov, Vladimir
In this paper we address several algebraic constructions in the context of groupoids, algebroids and $\mathbb Z$-graded manifolds. We generalize the results of integration of $\mathbb N$-graded Lie algebras to the honest $\mathbb Z$-graded case and p
Externí odkaz:
http://arxiv.org/abs/2207.07083
Publikováno v:
Math. Mech. Compl. Sys. 11 (2023) 1-18
We discuss the notion of basic cohomology for Dirac structures and, more generally, Lie algebroids. We then use this notion to characterize the obstruction to a variational formulation of Dirac dynamics.
Externí odkaz:
http://arxiv.org/abs/2109.00313
Autor:
Kotov, Alexei, Salnikov, Vladimir
In this paper we discuss the categorical properties of $\mathbb{Z}$-graded manifolds. We start by describing the local model paying special attention to the differences in comparison to the $\mathbb{N}$-graded case. In particular we explain the origi
Externí odkaz:
http://arxiv.org/abs/2108.13496
Autor:
Kotov, Alexei, Salnikov, Vladimir
Publikováno v:
In Differential Geometry and its Applications April 2024 93
Publikováno v:
Math. Mech. Compl. Sys. 9 (2021) 59-75
In this paper we make an overview of results relating the recent "discoveries" in differential geometry, such as higher structures and differential graded manifolds with some natural problems coming from mechanics. We explain that a lot of classical
Externí odkaz:
http://arxiv.org/abs/2007.11081
Autor:
Kotov, Alexei, Salnikov, Vladimir
Publikováno v:
In Journal of Geometry and Physics September 2023 191