# Alex Haro

### Biosketch

He did his PhD thesis under the supervision of professor Carles Simó (october 1998). Funded by the Fulbright program, he did a postdoctoral stay at the University of Texas at Austin, where he started a fruitful collaboration with professor Rafael de la Llave. He got a permanent position at UB in july 2001.

The main scientific achievement is the development of a singurality theory for KAM tori (jointly with Rafael de la Llave and Alejandra González), which involves tools from symplectic geometry and functional analysis, and leads to efficient algorithms of computation. This work has been recognised by professor M. Sevryuk as one of the main achievements in KAM theory during the last decade. He and Rafael de la Llave havealso discovered new mechanisms of breakdown of invariant tori.

### Research lines

- Dynamical systems
- Invariant manifolds
- KAM theory
- Computational dynamical systems
- Computer assisted proofs

### Selected publications

- A. Gonza?lez-Enri?quez, A. Haro, R. de la Llave. Singularity theory for non-twist KAM tori. 227, pp. 1 – 128. American Mathematical Society (AMS), 2014. ISBN 978-0-8218-9018-9
- A. Haro, J. Puig. Thouless formula and Aubry duality for long-range Schroedinger skew-products. Nonlinearity. 26 – 5, pp. 1163. IOP Pub., 2013. doi: 10.1088/0951-7715/26/5/1163. ISSN 0951-7715
- A. Haro, R. de la Llave. Manifolds on the verge of a hyperbolicity breakdown. Chaos. 16, pp. 013120. American Institute of Physics, 2006. ISSN 1054-1500
- J.L. Figueras, A. Haro. Reliable computation of robust response tori on the verge of breakdown. SIAM Journal On Applied Dynamical Systems. 11 – 2, pp. 597 – 628. Society for Industrial and Applied Mathematics., 2012. doi: 10.1137/100809222. ISSN 1536-0040
- A. Haro, R. de la Llave. A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps : rigorous results. Journal of Differential Equations. 228 – 2, pp. 530 – 579. Elsevier, 2006. ISSN 0022-0396