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| HAL : hal-00150953, version 2 |
| arXiv : 0706.0138 |
| DOI : 10.1007/s00574-011-0003-x |
| Fiche détaillée |  Récupérer au format |
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| Bulletin Brazilian Mathematical Society 42, 1 (2011) 45-74 |
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| Versions disponibles : | v1 (01-06-2007) | v2 (09-03-2011) |
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| A quasianalyticity property for monogenic solutions of small divisor problems |
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| Stefano Marmi 1David Sauzin 2 |
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| (2011) |
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| We discuss the quasianalytic properties of various spaces of functions suitable for one-dimensional small divisor problems. These spaces are formed of functions C^1-holomorphic on certain compact sets K_j of the Riemann sphere (in the Whitney sense), as is the solution of a linear or non-linear small divisor problem when viewed as a function of the multiplier (the intersection of K_j with the unit circle is defined by a Diophantine-type condition, so as to avoid the divergence caused by roots of unity). It turns out that a kind of generalized analytic continuation through the unit circle is possible under suitable conditions on the K_j's. |
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| 1 : | Gruppo di ricerca di sistemi dinamici (SNS PISA) |
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Scuola Normale Superiore |
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| 2 : | Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE) |
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CNRS : UMR8028 – INSU – Observatoire de Paris – Université Paris VI - Pierre et Marie Curie – Université des Sciences et Technologies de Lille - Lille I |
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| Domaine | : | Mathématiques/Systèmes dynamiques |
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| Borel's monogenic functions – quasianalyticity – small divisors |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00150953, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00150953 | |
| oai:hal.archives-ouvertes.fr:hal-00150953 | |
| Contributeur : David Sauzin | |
| Soumis le : Mercredi 9 Mars 2011, 10:40:44 | |
| Dernière modification le : Mercredi 9 Mars 2011, 17:22:26 | |
