Integrabilidad de sistemas no lineales hamiltonianos con N grados de libertad

  1. Alfonso Blasco Sanz
Supervised by:
  1. Ángel Ballesteros Castañeda Director

Defence university: Universidad de Burgos

Year of defence: 2009

Committee:
  1. Mariano Santander Navarro Chair
  2. Francisco José Herranz Zorrilla Secretary
  3. Enrico Geleghini Committee member
  4. Luis Román Rodríguez Cano Committee member
  5. Otto Rutwig Campoamor Committee member
Department:
  1. Física

Type: Thesis

Abstract

This Ph.D. Thesis presents the construction of new completely integrable classical Hamiltonian systems with N degrees of freedom through the coalgebra symmetry approach. Firstly, we have obtained the necessary integrability condition for a symplectic realization of any Poisson coalgebra, which has been systematically explored for dimensions 3,4,5 and 6. The associated integrable systems have been fully described. Secondly, the ¨two-photon¨ algebra has been used to introduce many new families of quasi-integrable Hamiltonians in N dimensions, including natural systems, geodesic flows and electromagnetic Hamiltonians. Some of them have been shown to be completely integrable through different algebraic techniques. As outstanding examples, two new families of nonlinear perturbations of the N-dimensional harmonic oscillator have been introduced. Finally, N dimensional generalizations of two-dimensional integrable systems have been presented by making use of the coalgebra approch. In particular, new generalized Hénon-Heiles systems, Ramani potentials and coupled ND quartic oscillators have been constructed.