Bounemoura Abed - CV

CEREMADE

Bounemoura Abed

Chargé de recherche CNRS

Biographie

Abed Bounemoura is interested in the perturbation theory of integrable Hamiltonian systems. He plans to further investigate, theoretically and on concrete examples, the stability and instability properties of those systems.

Publications

BU Paris-Dauphine

Articles

Bounemoura A. (2019), Some remarks on the optimality of the Bruno-Rüssmann condition, Bulletin de la Société mathématique de France, vol. 147, n°2, p. 341-353

Bounemoura A., Fayad B., Niederman L. (2019), Nekhoroshev estimates for steep real-analytic elliptic equilibrium points, Nonlinearity, vol. 33, n°1

Bounemoura A., Féjoz J. (2019), KAM, α -Gevrey regularity and the α -Bruno-Rüssmann condition, Annali della Scuola Normale Superiore di Pisa. Classe di Scienze, vol. 19, n°4, p. 1225-1279

Bounemoura A., Féjoz J. (2018), Hamiltonian perturbation theory for ultra-differentiable functions, Memoirs of the American Mathematical Society

Bounemoura A., Fayad B., Niederman L. (2017), Superexponential Stability of Quasi-Periodic Motion in Hamiltonian Systems, Communications in Mathematical Physics, vol. 350, n°1, p. 361–386

Bounemoura A. (2017), Some instability properties of resonant invariant tori in Hamiltonian systems, Mathematical Research Letters, vol. 24, n°1, p. 21-35

Bounemoura A. (2016), Non-degenerate Liouville tori are KAM stable, Advances in Mathematics, vol. 292, p. 42-51

Bounemoura A., Kaloshin V. (2016), A note on micro-instability for Hamiltonian systems close to integrable, Proceedings of the American Mathematical Society, vol. 144, p. 1553-1560

Bounemoura A. (2016), Non-degenerate Liouville tori are KAM stable, Advances in Mathematics, vol. 292, p. 42-51

Bounemoura A. (2016), Nekhoroshev’s estimates for quasi-periodic time-dependent perturbations, Commentarii Mathematici Helvetici, vol. 91, n°4, p. 653-703

Bounemoura A. (2016), Ergodization time for linear flows on tori via geometry of numbers, Archiv der Mathematik, vol. 106, n°2, p. 129-133

Bounemoura A. (2016), Generic perturbations of linear integrable Hamiltonian systems, Regular and Chaotic Dynamics, vol. 21, n°6, p. 665-681

Bounemoura A. (2014), A KAM Theorem through Dirichlet's Box and Khintchine's Transference Principles, Moscow Mathematical Journal, vol. 14, n°4, p. 697-709

Bounemoura A., Fischler S. (2014), The classical KAM theorem for Hamiltonian systems via rational approximations, Regular and Chaotic Dynamics, vol. 19, n°2, p. 251-265

Bounemoura A., Kaloshim V. (2014), Generic Fast Diffusion for a Class of Non-Convex Hamiltonians with Two Degrees of Freedom, Moscow Mathematical Journal, vol. 14, n°2, p. 181-203

Berger P., Bounemoura A. (2013), A geometrical proof of the persistence of normally hyperbolic submanifolds, Dynamical Systems, vol. 28, n°4, p. 567-581

Bounemoura A. (2013), Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians, Regular and Chaotic Dynamics, vol. 18, n°3, p. 261-276

Bounemoura A., Fischler S. (2013), A Diophantine duality applied to the KAM and Nekhoroshev theorems, Mathematische Zeitschrift, vol. 275, n°3-4, p. 1135-1167

Bounemoura A. (2013), Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians, Regular and Chaotic Dynamics, vol. 18, n°3, p. 237-260

Bounemoura A., Pennamen E. (2012), Instability for a priori unstable Hamiltonian systems: A dynamical approach, Discrete and Continuous Dynamical Systems. Series A, vol. 32, n°3, p. 753-793

Bounemoura A. (2012), Optimal Stability and Instability for Near-Linear Hamiltonians, Annales Henri Poincaré, vol. 13, n°4, p. 857-868

Prépublications / Cahiers de recherche

Bounemoura A., Fayad B., Niederman L. (2019), Super-exponential stability for generic real-analytic elliptic equilibrium points, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 25 p.

Bounemoura A. (2018), Positive measure of KAM tori for finitely differentiable Hamiltonians, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 20 p.

Bounemoura A. (2018), Some remarks on the optimality of the Bruno-Rüssmann condition, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 12 p.

Bounemoura A., Fayad B., Niederman L. (2015), Double exponential stability for generic real-analytic elliptic equilibrium points, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 51 p.

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