Zobrazeno 1 - 10 of 37 pro vyhledávání: '"Abed Bounemoura"'
1
Reducibility of ultra-differentiable quasiperiodic cocycles under an adapted arithmetic condition
Autor: Claire Chavaudret, Shuqing Liang, Abed Bounemoura
Publikováno v: Proceedings of the American Mathematical Society. 149:2999-3012
We prove a reducibility result for sl(2,R) quasi-periodic cocycles close to a constant elliptic matrix in ultra-differentiable classes, under an adapted arithmetic condition which extends the Brjuno-Russmann condition in the analytic case. The proof
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a64cc37562cc8c0fcf0b3822b7d645b8
https://doi.org/10.1090/proc/15433
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2
Positive measure of KAM tori for finitely differentiable Hamiltonians
Autor: Abed Bounemoura
Publikováno v: Journal de l’École polytechnique — Mathématiques. 7:1113-1132
Consider an integer $n \geq 2$ and real numbers $\tau>n-1$ and $l>2(\tau+1)$. Using ideas of Moser, Salamon proved that individual Diophantine tori persist for Hamiltonian systems which are of class $C^l$. Under the stronger assumption that the syste
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ce68cae5dba0a0f6d95e1a776276a653
https://doi.org/10.5802/jep.137
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3
KAM, α-Gevrey regularity and the α-Bruno-Rüssmann condition
Autor: Jacques Féjoz, Abed Bounemoura
Publikováno v: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. :1225-1279
We prove a new invariant torus theorem, for α-Gevrey smooth Hamiltonian systems , under an arithmetic assumption which we call the α-Bruno-Russmann condition , and which reduces to the classical Bruno-Russmann condition in the analytic category. Ou
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f9ca66a59c27a3ddf0c573cc881afcb8
https://doi.org/10.2422/2036-2145.201707_009
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4
Nekhoroshev estimates for steep real-analytic elliptic equilibrium points
Autor: Laurent Niederman, Abed Bounemoura, Bassam Fayad
Publikováno v: HAL
Nonlinearity
Nonlinearity, IOP Publishing, In press
Nonlinearity, 2020, ⟨10.1088/1361-6544/ab4c89⟩
Nonlinearity, IOP Publishing, 2020, 33 (1), pp.1-33. ⟨10.1088/1361-6544/ab4c89⟩
Nonlinearity, 2020, 33 (1), pp.1-33. ⟨10.1088/1361-6544/ab4c89⟩
International audience; We prove that steep real-analytic elliptic equilibrium points are exponentially stable, generalizing results which were known only under a convexity assumption. This proves the general case of a conjecture of Nekhoroshev. This
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::08af437c078a987c3f0c705587f04123
https://doi.org/10.1088/1361-6544/ab4c89
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5
Some remarks on the optimality of the Bruno-Rüssmann condition
Autor: Abed Bounemoura
Publikováno v: Bulletin de la société mathématique de France
Bulletin de la société mathématique de France, Société Mathématique de France, 2019, 147 (2), pp.341-353
International audience; We prove that the Bruno-Rüssmann condition is optimal for the analytic preservation of a quasi-periodic invariant curve for an analytic twist map. The proof is based on Yoccoz's corresponding result for analytic circle diffeo
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::81ad8f543583b4cb5c00c97818653606
https://doi.org/10.24033/bsmf.2784
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6
Hamiltonian perturbation theory for ultra-differentiable functions
Autor: Abed Bounemoura, Jacques Féjoz
Publikováno v: Memoirs of the American Mathematical Society. 270
Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means of hard i
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::e49066d45f14eceb5d5e462859b346bb
https://doi.org/10.1090/memo/1319
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7
Super-exponential stability for generic real-analytic elliptic equilibrium points
Autor: Abed Bounemoura, Laurent Niederman, Bassam Fayad
Publikováno v: Advances in Mathematics
Advances in Mathematics, Elsevier, 2020, 366
Advances in Mathematics, 2020, 366, ⟨10.1016/j.aim.2020.107088⟩
HAL
International audience; We consider the dynamics in a neighborhood of an elliptic equilibrium point with a Diophantine frequency of a symplectic real analytic vector field and we prove the following result of effective stability. Generically, both in
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::625e53f76df2039b7b45d1adc30ef2aa
https://hal.archives-ouvertes.fr/hal-01188980v2/document
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10
Generic perturbations of linear integrable Hamiltonian systems
Autor: Abed Bounemoura
Publikováno v: Regular and Chaotic Dynamics
Regular and Chaotic Dynamics, MAIK Nauka/Interperiodica, 2016, 21 (6), pp.665-681. ⟨10.1134/S1560354716060071⟩
Regular and Chaotic Dynamics, 2016, 21 (6), pp.665-681. ⟨10.1134/S1560354716060071⟩
International audience; In this paper, we investigate perturbations of linear integrable Hamiltonian systems, with the aim of establishing results in the spirit of the KAM theorem (preservation of invariant tori), the Nekhoroshev theorem (stability o
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6d924513e96f3587adae202a0e26007e
https://doi.org/10.1134/s1560354716060071
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