Análisis de algunas degeneraciones y de bifurcaciones globales en campos vectoriales simétricos

  1. Manuel Merino Morlesin
Supervised by:
  1. Antonio Algaba Durán Director
  2. Alejandro J. Rodríguez-Luis Director

Defence university: Universidad de Huelva

Year of defence: 2009

  1. Emilio Freire Macías Chair
  2. Cristóbal García García Secretary
  3. Fernando Fernández Sánchez Committee member
  4. Estanislao Gamero Gutiérrez Committee member
  5. Eusebius Doedel Committee member

Type: Thesis


Hopf-silla-nodo. Chapter 1 is devoted to analyze linear degenerations of equilibria in Chua�s equation. Some aspects associated with bifurcations exhibited by Chua�s equation in a neighbourhood of the Hopf-pitchfork linear degeneracy are considered in Chapter 2. In Chapter 3 a numerical analysis of the resonance zones, that exist in relationship with a torus curve, is performed. Chapter 4 is devoted to analyze the bifurcation behaviour of Shil�nikov homoclinic connections in Z2-symmetric systems. The study of the triple-zero bifurcation is the core of Chapter 5. A three-parametric unfolding of this linear degeneration for systems with Z2-symmetry is considered. In Chapter 6 we analyze the saddle-node and cusp bifurcations of periodic orbits, of a curve of codimension-two heteroclinic connections. Last chapter is motivated by the theoretical study of a degenerate Hopf-saddle-node bifurcation.