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Research


My research focuses on the following areas:


Preprints and Publications

  1. with Ohlson Timoudas, T. Sharp 1/2-Holder continuity of the Lyapunov exponent at the bottom of the spectrum for a class of Schrodinger operators. (Submitted). Preprint version

  2. with Haro, A. and Luque, A. Effective bounds for the Measure of Rotations. (Submitted). Preprint version

  3. with Strängberg, D. Non-Smooth Bifurcations of Uniformly Hyperbolic Invariant Manifolds in Skew Product Systems: Rigorous Results. (Accepted in Nonlinearity). Preprint version

  4. On the sharpness of the Russmann estimates.
    Figueras, J-Ll., Haro, A. and Luque, A..
    Commun Nonlinear Sci Numer Simat, 55, (2018), 42-55.
    Preprint version

  5. A Framework for the Numerical Computation and a Posteriori Verification of Invariant Objects of Evolution Equations.
    Figueras, J-Ll., Gameiro, M., Lessard, J-P, de la Llave, R.
    SIAM J. Appl. Dyn. Syst. 16, 2 (2017), pp. 1070-1088.
    Preprint version

  6. Numerical Computations and Computer Assisted Proofs of Periodic Orbits of the Kuramoto-Sivashinsky Equation.
    Figueras, J-Ll., de la Llave, R.
    SIAM J. Appl. Dyn. Syst. 16, 1 (2017), pp. 834-852.
    Preprint version

  7. Rigorous computer assisted application of KAM theory: a modern approach.
    Figueras, J-Ll., Haro, A., Luque, A.
    Foundations of Computational Mathematics, 17, 5, pp. 1123-1193, (2017). Preprint version

  8. A note on the fractalization route for saddle invariant curves in quasiperiodic systems.
    Figueras, J-Ll., Haro, A.,
    Discrete and Continuous Dynamical Systems - Series S, vol. 9, 4 (2016), pp. 1095-1107. Special volume in Nonautonomous Dynamics, (2016).

  9. (Book) The Parameterization method for Invariant Manifolds: From Rigorous Results to Effective Computations.
    Canadell, M., Figueras, J-Ll., Haro, A., Luque, A., Mondelo, J. M.,
    Applied Mathematical Sciences, Springer, (2016).

  10. Different scenarios for hyperbolicity in quasiperiodic area preserving twist maps.
    Figueras, J-Ll., Haro, A.,
    Chaos: An Interdisciplinary Journal of Nonlinear Science, 25, 12 (2015), 16 pages.

  11. Triple Collisions of invariant bundles.
    Figueras, J-Ll., Haro, A.,
    Discrete and Continuous Dynamical Systems - Series B, vol. 18, 8 (2013), pp. 2069-2082.

  12. Computer-assisted techniques for the verification of the Chebyshev property of Abelian integrals.
    Figueras, J-Ll., Tucker, W., Villadelprat, J.,
    Journal of Differential Equations, 254, (2013), pp. 3647-3663.

  13. Collision of invariant bundles of quasi-periodic attractors in the dissipative standard map.
    Calleja, R., Figueras, J-Ll.,
    Chaos, An Interdisciplinary Journal of Nonlinear Science, 22, 3, (2012), 11 pages.
    Preprint version.

  14. Reliable computation of robust response tori on the verge of breakdown.
    Figueras, J-Ll., Haro, A.
    SIAM J. Appl. Dyn. Syst. 11 (2012), pp. 597-628.
    Preprint version

Ph.D. Thesis

  1. Fiberwise Hyperbolic Invariant Tori in quasiperiodically skew product systems. Universitat de Barcelona, Ph.D. Thesis (May 2011), Supervisor: Àlex Haro


(September 17, 2018 by Jordi-Lluís Figueras)