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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.13216 |
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| _version_ | 1866913946774011904 |
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| author | Fauvet, Frédéric Menous, Frédéric Sauzin, David |
| author_facet | Fauvet, Frédéric Menous, Frédéric Sauzin, David |
| contents | We provide explicit formulas of non-recursive type for the
linearizing transformations of a non-resonant analytic germ of
diffeomorphism at a fixed point or a non-resonant analytic germ of
vector field at a singular point, in any complex dimension.
The formal expressions we obtain rely on a part of Ecalle's
tree-based combinatorics called ``armould calculus" and they have
the same shape for dynamical systems with discrete or continuous
time.
They allow us to recover in a straightforward manner, under Bruno's
arithmetical condition,
the best known estimates for the domains of convergence of the
analytic linearizing changes of variables
in terms of the value of the Bruno series,
including a new precise dependence with respect to the dimension of
the problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13216 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit linearization of multi-dimensional germs and vector fields through Ecalle's tree expansions Fauvet, Frédéric Menous, Frédéric Sauzin, David Dynamical Systems We provide explicit formulas of non-recursive type for the linearizing transformations of a non-resonant analytic germ of diffeomorphism at a fixed point or a non-resonant analytic germ of vector field at a singular point, in any complex dimension. The formal expressions we obtain rely on a part of Ecalle's tree-based combinatorics called ``armould calculus" and they have the same shape for dynamical systems with discrete or continuous time. They allow us to recover in a straightforward manner, under Bruno's arithmetical condition, the best known estimates for the domains of convergence of the analytic linearizing changes of variables in terms of the value of the Bruno series, including a new precise dependence with respect to the dimension of the problem. |
| title | Explicit linearization of multi-dimensional germs and vector fields through Ecalle's tree expansions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2507.13216 |