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Research

My research focuses on the following areas:

• Skew products of area-preserving maps on the fiber and Aperiodic Dense Orbit maps on the base.
• Study of the breakdown of normally hyperbolic invariant tori.
• Computer Assisted proofs in Dynamical Systems.
• Rigorous numerics for PDEs.
• A-posteriori KAM theory.

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. Non-Smooth Bifurcations of Uniformly Hyperbolic Invariant Manifolds in Skew Product Systems.
   Figueras, J-Ll. and Lilja, D.
   Nonlinearity, 31, (2018), 5573-5588. 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

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