José Pedro Gaivão

CEMAPRE, ISEG - Universidade de Lisboa
Rua do Quelhas, 6
1200-781 Lisboa

Email: jpgaivao at
Phone: (+351) 213 925 874 (Ext. 3874)
Office: 511, Quelhas 6

I am a postdoc fellow at CEMAPRE based at ISEG, Portugal. I am also a member of the Lisbon Dynamical Systems Group - LxDS.

Research interests:

Dynamical Systems, particularly Hamiltonian dynamics, billiards and exponentially small phenomena.


Licenciatura in Matemática Aplicada à Tecnologia, Universidade do Porto (2005)
PhD in Mathematics (supervisor: Vassili Gelfreich), University of Warwick (2010)


  1. Exponentially small splitting of invariant manifolds near a Hamiltonian-Hopf bifurcation
    PhD thesis, University of Warwick, 2010.
  2. Splitting of separatrices for the Hamiltonian-Hopf bifurcation with the Swift-Hohenberg equation as an example
    (with V. Gelfreich).
    Nonlinearity, 24, no.3, p. 677-698, 2011.
  3. Chaos in the square billiard with a modified reflection law
    (with G. Del Magno, J. L. Dias, P. Duarte and D. Pinheiro).
    Chaos, 22, 026106, 2012.
  4. Analytic invariants for the 1:-1 resonance.
    Annales de l'Institut Fourier, vol. 63, no.4, p. 1267-1426, 2013.
  5. SRB measures for polygonal billiards with contracting reflection laws
    (with G. Del Magno, J. L. Dias, P. Duarte and D. Pinheiro).
    Communications in Mathematical Physics, vol. 329, 2, p. 687-723, 2014.
  6. Ergodicity of polygonal slap maps
    (with G. Del Magno, J. L. Dias and P. Duarte).
    Nonlinearity, 27, no.8, p. 1969-1983, 2014.
  7. Dissipative outer billiards: a case study
    (with G. Del Magno and E. Gutkin),
    Dynamical Systems: An International Journal, vol. 30, no.1, p. 45-69, 2015.
  8. Hyperbolic polygonal billiards with finitely many ergodic SRB measures
    (with G. Del Magno, J. L. Dias, P. Duarte).
    Ergodic Theory and Dynamical Systems, 1-24, doi:10.1017/etds.2016.119, 2017.
  9. Hyperbolic billiards on polytopes with contracting reflection laws
    (with P. Duarte and M. Soufi).
    Discrete and Continuous Dynamical Systems - Series A, vol. 37, no. 6, p. 3079-3109, 2017.
  10. Ergodic properties of polygonal billiards with strongly contracting reflection laws
    (with G. Del Magno, J. L. Dias, P. Duarte).
    Preprint, 2015.
  11. $\lambda$-stability of periodic bililard orbits
    (with S. Troubetzkoy).
    Preprint, 2016.
  12. Renormalization of Gevrey vector fields with a Brjuno type aithmetical condition
    (with J. L. Dias).
    Preprint, 2017.
  13. Asymptotic periodicity in outer billiards with contraction
    Preprint, 2017.

Conference proceedings:

  1. Practical implementation issues for switching between stabilizing controllers
    (with E. Santos, T. Mendonça and P. Rocha).
    Proc. of the 7th Portuguese Conference on Automatic Control, M. Ayala-Botto, IST, 6 p., Lisbon, Portugal, September 11-13, 2006.
  2. Observer design in switching control of neuromuscular blockade: clinical cases
    (with H. Magalhães, J. Lemos, T. Mendonça, P. Rocha and S. Esteves).
    28th Annual International Conference IEEE Engineering in Medicine and Biology Proceedings, p. 5436-5439, 2006.
  3. Exponentially small splitting of separatrices.
    Bol. Soc. Port. Mat. Special Issue , p. 181-184, 2012.
  4. Polygonal billiards with a contractive reflection law: a review of some hyperbolic properties
    (with G. Del Magno, J. L. Dias, P. Duarte and D. Pinheiro)
    in Difference Equations, Discrete Dynamical Systems and Applications, Eds. L. Alseda i Soler et al., Springer Proceedings in Mathematics and Statistics 180, 2016.