Person: Martínez Ontalba, Celia
Universidad Complutense de Madrid
Faculty / Institute
Álgebra, Geometría y Topología
Geometría y Topología
Now showing 1 - 5 of 5
- PublicationLie symmetries versus integrability in evolution equations(IOP Publishing, 1993) Abellanas, L.; Martínez Ontalba, CeliaMotivated by some recent results obtained concerning the invariance properties of a particular family of generalized KdV equations, we investigate the possible significance of classical Lie invariance groups as a test for complete integrability.
- PublicationArnold’s conjecture and symplectic reduction(Elsevier, 1996) Ibort, A.; Martínez Ontalba, CeliaFortune (1985) proved Arnold's conjecture for complex projective spaces, by exploiting the fact that CPn-1 is a symplectic quotient of C-n. In this paper, we show that Fortune's approach is universal in the sense that it is possible to translate Arnold's conjecture on any closed symplectic manifold (Q,Omega) to a critical point problem with symmetry on loops in R(2n) With its Standard symplectic structure.
- PublicationPolynomial translation moduies and Casimir invariants(IOP Publishing, 1993) Abellanas, L.; Martínez Alonso, Luis; Martínez Ontalba, CeliaWe give a positive answer to a question about the existence of any direct link between two apparently unrelated facts for a specific family of solvable Lie algebras: the structure of their modules of functions on one side, and the algebraic form of their Casimir invariants on the other.
- PublicationOn the structure of the moduli of jets of G-structures with a linear connection(Elsevier Science, 2003) Martínez Ontalba, Celia; Muñoz Masqué, Jaime; Valdés Morales, AntonioThe moduli space of jets of G-structures admitting a canonical linear connection is shown to be isomorphic to the quotient by G of a natural G-module.
- PublicationPeriodic orbits of Hamiltonian systems and symplectic reduction(IOP Publishing, 1996) Ibort, A.; Martínez Ontalba, CeliaThe notion of relative periodic orbits for Hamiltonian systems with symmetry is discussed and a correspondence between periodic orbits of reduced and unreduced Hamiltonian systems is established. Variational principles with symmetries are studied from the point of view of symplectic reduction of the space of loops, leading to a characterization of reduced periodic orbits by means of the critical subsets of an action functional restricted to a submanifold of the loop space of the unreduced manifold. Finally, as an application, it is shown that if the symplectic form ! has finite integral rank, then the periodic orbits of a Hamiltonian system on the symplectic manifold .M; !/ admit a variational characterization.