40 citations · 196 across the 18 of their papers we have counts for
18 papers
On Darboux theorems for geometric structures induced by closed forms
Xavier Gràcia, Javier de Lucas, Xavier Rivas +1
This work reviews the classical Darboux theorem for symplectic, presymplectic, and cosymplectic manifolds (which are used to describe regular and singular mechanical systems), and…
Reduction and reconstruction of multisymplectic Lie systems
Javier de Lucas, Xavier Gràcia, Xavier Rivas +2
A Lie system is a non-autonomous system of first-order ordinary differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dim…
Poisson-Hopf deformations of Lie-Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra
Angel Ballesteros, Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz +2
The formalism for Poisson-Hopf (PH) deformations of Lie-Hamilton systems is refined in one of its crucial points concerning applications, namely the obtention of effective and comp…
Geometric models for Lie--Hamilton systems on
J. Lange, J. de Lucas
This paper provides a geometric description for Lie--Hamilton systems on with locally transitive Vessiot--Guldberg Lie algebras through two types of geometric models…
Multisymplectic structures and invariant tensors for Lie systems
X. Gràcia, J. de Lucas, M. C. Muñoz-Lecanda +1
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 algebr…
On the geometry of the Clairin theory of conditional symmetries for higher-order systems of PDEs with applications
A. M. Grundland, J. de Lucas
This work presents a geometrical formulation of the Clairin theory of conditional symmetries for higher-order systems of partial differential equations (PDEs). We devise methods fo…