Jaume Llibre

Full professor at UAB
Research area: Dynamical Systems
Personal webpage

PhD in Mathematics obtained at UAB

Biosketch

He has devloped his research mainly at UAB. He began his research on celestial mechanics and Hamiltonian systems. Then became interested in discrete dynamical systems, and in the qualitative theory of ordinary differential equations. He has contributed to the formation of the group of mathematicians working at dynamical systems at UAB, see the website: http://www.gsd.uab.cat/

Current and previous positions

Profesor Ajudant Universidad de Barcelona, 1974-75
Profesor Encarregat de Curs, UAB. 1975-76
Profesor Adjunt Interi, UAB, 1976-79
Profesor Agregad Interi,UAB, 1979-82
Profesor Adjunt Numerari (encarregat de Càtedra),UAB, 1982-86
Profesor Catedràtic de Universistat, UAB, 1986-

Prizes, awards, honors, distinctions

Acadèmic de la Reial Acadèmia de Ciències i Arts de Barcelona, 2002-
ICREA Academia, 2009-2014
Excellent Visiting Professor for the Universidade de Sao Paulo, 2014-2016
Excellent Visiting Professor for the Shanghai Jiao Tong University, 2014-2016
Medalla Narcís Monturial al mèrit científic i tecnològic, 2015

 

Research lines

The main topics of his research have been and are the dynamics of the n-body problem, integrability of differential systems, periodic orbits of differential systems, and in particular the Hilbert’s 16th problem, the problem of distinguishing between a center and a focus, the periodic structure of certain classes of functions and their topological entropy in lower and higher dimensional spaces.

Selected publications

  • Higher order averaging theory for finding periodic solutions via Brouwer degree, Nonlinearity 27 (2014), 563-583, (with D.D. Novaes and M.A. Teixeira)
  • On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves, J. Differential Equations 250 (2010), 983-999, (with R. Ramírez and N. Sadovskaia)
  • Darboux Theory of Integrability in C^n taking into account the multiplicity, J. of Differential Equations 246 (2009), 541-551, (with Xiang Zhang)
  • Multiplicity of invariant algebraic curves in polynomial vector fields, Pacific J. Math. 229 (2007), 63-117 (with C. Christopher and J. Pereira)
  • Configurations of limit cycles and planar polynomial vector fields, J. Differential Equations 198 (2004), 374-380 (with G. Rodríguez)