A new quasi-analytic class
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909034345398272 |
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| author | Garay, Mauricio van Straten, Duco |
| author_facet | Garay, Mauricio van Straten, Duco |
| contents | Spaces of quasi-analytic classes are defined by the existence and uniqueness of Taylor expansions, which are not necessarily convergent. First examples were given by Borel in his theory of monogenic functions, a generalisation of holomorphic functions defined on locally closed sets. Denjoy and Carleman then gave simpler examples of quasi-analytic classes which are now widely known. Unfortunately, in most examples coming from mathematical physics and number theory, the power series are neither of Borel nor Denjoy-Carleman's classes. In this paper we introduce a quasi-analytic class which is relevant to perturbation theory and especially to KAM theory and dynamical systems. Our theorems also explain geometrically the divergence of most perturbative expansions by the presence of accumulation points of poles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04583 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new quasi-analytic class Garay, Mauricio van Straten, Duco Complex Variables Dynamical Systems 26E10, 37J40 Spaces of quasi-analytic classes are defined by the existence and uniqueness of Taylor expansions, which are not necessarily convergent. First examples were given by Borel in his theory of monogenic functions, a generalisation of holomorphic functions defined on locally closed sets. Denjoy and Carleman then gave simpler examples of quasi-analytic classes which are now widely known. Unfortunately, in most examples coming from mathematical physics and number theory, the power series are neither of Borel nor Denjoy-Carleman's classes. In this paper we introduce a quasi-analytic class which is relevant to perturbation theory and especially to KAM theory and dynamical systems. Our theorems also explain geometrically the divergence of most perturbative expansions by the presence of accumulation points of poles. |
| title | A new quasi-analytic class |
| topic | Complex Variables Dynamical Systems 26E10, 37J40 |
| url | https://arxiv.org/abs/2410.04583 |