Juan Ramón Pacha

Lecturer at UPC
Research area: Dynamical Systems

PhD in Mathematics obtained at UPC


BSc (licenciado, Universitat de Barcelona) in Physics and PhD (UPC) in Mathematics has developed his academic and research tasks at the Universitat Politècnica de Catalunya. His research is focused in the study of Dynamical Systems. In this field, he has achieved some results concerning quasi periodic bifurcation phenomena, and the analysis of normal forms of Hamiltonian systems in the neighborhood of non semi-simple resonances. Currently he works on the study of homoclinic connections in Hamiltonian PDE as well as on applications in Celestial Mechanics.

Research lines

  • Dynamical Systems
  • KAM theory
  • Celestial Mechanics
  • Engineering Mathematics

Selected publications

  • Ollé, M.; Pacha, J.R. and Villanueva, J.: Quantitative estimates on the normal form around a non-semi-simple 1:-1 resonant periodic orbit. Nonlinearity, 18(3): 1141-1172, 2005
  • Ollé, M.; Pacha, J.R. and Villanueva, J.: Kolmogorov-Arnold-Moser aspects of the periodic Hamiltonian Hopf bifurcation. Nonlinearity, 21(8):1759-1811, 2008
  • Delshams, A.; Gutiérrez, P.; Koltsova, O. and Pacha, J.R.: Transverse intersec¬tions between invariant manifolds of double hyperbolic invariant tori, via the Poincaré-Mel’nikov method. Regul. Chaotic Dyn., 15(2-3):222-236, 2010
  • Delshams, A.; Gutiérrez, P. and Pacha, J.R.: Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via Hamiltom-Jacobi equa¬tion. Phys. D, 243:64-85, 2013