Zobrazeno 1 - 10
of 109
pro vyhledávání: '"Vilariño, S."'
Publikováno v:
J. Geom. Phys. 191, 104899 (2023)
We review and slightly improve the known k-polysymplectic Marsden--Weinstein reduction theory by removing some technical conditions on k-polysymplectic momentum maps by developing a theory of affine Lie group actions for k-polysymplectic momentum map
Externí odkaz:
http://arxiv.org/abs/2302.09037
A Lie system is the non-autonomous system of differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional Lie algebra of vector fields, a so-called Vessiot--Guldberg Lie algebra. This wo
Externí odkaz:
http://arxiv.org/abs/1808.06240
Publikováno v:
J.Math.Anal.Appl. 440 (2016) no. 1 394-414
This work presents and studies Riccati equations over finite-dimensional normed division algebras. We prove that a Riccati equation over a finite-dimensional normed division algebra $A$ is a particular case of conformal Riccati equation on a Euclidea
Externí odkaz:
http://arxiv.org/abs/1603.01413
Publikováno v:
Int. J. Geom. Methods Mod. Phys. 12, 1550071 (2015)
The $k$-symplectic structures appear in the geometric study of the partial differential equations of classical field theories. Meanwhile, we present a new application of the $k$-symplectic structures to investigate a type of systems of first-order or
Externí odkaz:
http://arxiv.org/abs/1412.5161
This book is devoted to review two of the most relevant approaches to the study of classical field theories of first order, say k-symplectic and k-cosymplectic. In the last part, we relate the k-symplectic and k-cosymplectic manifolds with the multis
Externí odkaz:
http://arxiv.org/abs/1409.5604
Autor:
de Lucas, J., Vilariño, S.
Publikováno v:
J. Differential Equations 258 (6), 2221--2255 (2015)
A Lie system is a system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of vector fields: a so-called Vessiot-Guldberg Lie algebra.
Externí odkaz:
http://arxiv.org/abs/1404.1596
Autor:
de León, M., Vilariño, S.
In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for time dependent Mechanics to the case of classical field theories in the k-cosymplectic framework.
Externí odkaz:
http://arxiv.org/abs/1304.3360
Autor:
de León, M., Vilariño, S.
In this paper we extend the well-know normal form theorem for Lagrangian submanifolds proved by A. Weinstein in symplectic geometry to the setting of k-symplectic manifolds.
Externí odkaz:
http://arxiv.org/abs/1202.3964
Publikováno v:
Publ. Math. Debrecen 78(2) (2011), 297-316
The canonical k-tangent structure on $T^1_kQ=TQ\oplus\stackrel{k}...\oplus TQ$ allows us to characterize nonlinear connections on $T^1_kQ$ and to develop G\"unther's (k-symplectic) Lagrangian formalism. We study the relationship between nonlinear con
Externí odkaz:
http://arxiv.org/abs/1109.5830
Publikováno v:
J. Math. Phys. 52(2), 022901 (2011) (20 pages)
This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating conservation laws to
Externí odkaz:
http://arxiv.org/abs/1009.2703