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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, Volume 27, Number 3, Pages 271–285
DOI: https://doi.org/10.21538/0134-4889-2021-27-3-271-285 (Mi timm1856) 		 
Wilcox Formula for Vector Fields on Banach Manifolds

Yuri S. Ledyaevab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Western Michigan University
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DOI: https://doi.org/10.21538/0134-4889-2021-27-3-271-285
Abstract: We obtain an analogue of Wilcox-Snyder formula for flows of diffeomorphisms of $C^m$-smooth vector fields on infinite-dimensional Banach manifolds. For classical linear system this formula can be efficiently used, for example, to obtain Magnus expansion of solutions. The generalized Wilcox formula is obtained by using an extended Chronological Calculus for Banach manifold. We apply this formula to derive new structured differential equations which solutions approximate solutions of the original differential equation.
Keywords: flow of diffeomorphisms, Wilcox formula, chronological calculus, Magnus expansion.
Received: 20.07.2021
Revised: 11.08.2021
Accepted: 23.08.2021
Bibliographic databases:
Document Type: Article
MSC: 93C10, 45G15
Language: English
Citation: Yuri S. Ledyaev, “Wilcox Formula for Vector Fields on Banach Manifolds”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 3, 2021, 271–285
Citation in format AMSBIB
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\by Yuri~S.~Ledyaev
\paper Wilcox Formula for Vector Fields on Banach Manifolds
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2021
\vol 27
\issue 3
\pages 271--285
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