Amadeu Delshams

PhD in Mathematics from UB
Research areas: Dynamical Systems

I am a member of the UPC Dynamical Systems Group and the DANCE network.
I am a member of the Editorial Board of several Journals: Boletín SeMA, Discrete and Continuous Dynamical Systems, Gaceta de la RSME, Journal of Nonlinear Science, NoDEA Nonlinear Differential Equations and Applications.
I am/was involved in organizing several events: the CRM Research Program SIMS08, the AIMS Conferences, the first Iberian Mathematical Meeting, the Carles Simó Fest, the DANCE meetings Ddays, the Spanish meetings Nolineal, the DANCE Winter Schools RTNS, the Workshops of Interact between Dynamical Systems and PDE JISD, as well as other events of our group.
I have been Invited speaker in a number of conferences, like the 6th European Congress of Mathematics, Krakow, 2012, SIAM DSPDES’s, Barcelona, 2010, etc.

Research lines

  • Effective stability of Hamiltonian and reversible systems
  • Whiskered tori
  • Hyperbolic invariant objects
  • Splitting of separatrices
  • Arnold diffusion

Selected publications

  • Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation. A. Delshams, P. Gutiérrez, J.R. Pacha, Phys. D 243:64-85, 2013.
  • Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems. A. Delshams, G. Huguet, Nonlinearity, 22:1997-2077, 2009.
  • Geometric properties of the scattering map of a normally hyperbolic invariant manifold. A. Delshams, R. de la Llave, T. M. Seara. Adv. Math., 217(3): 1096-1153, 2008.
  • Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows. A. Delshams, R. de la Llave, T. M. Seara, Adv. Math., 202(1):64-188, 2006.
  • A Geometric Mechanism for Diffusion in Hamiltonian Systems Overcoming the large Gap Problem: Heuristics and Rigorous Verification on a Model. A. Delshams, R. de la Llave, T. M. Seara, Mem. Amer. Math. Soc., 179(844):1-141, 2006.