The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations
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Publication:1091532
DOI10.1016/0022-1236(87)90091-7zbMath0623.34058OpenAlexW1964300374MaRDI QIDQ1091532
Publication date: 1987
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0022-1236(87)90091-7
Lie algebras of Lie groups (22E60) Asymptotic expansions of solutions to ordinary differential equations (34E05) Local differential geometry (53B99)
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Cites Work
- On Carnot-Caratheodory metrics
- Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula
- Analytic vectors
- Formal differential equations
- Some aspects of differential geometry associated with hypoelliptic second order operators
- Balls and metrics defined by vector fields. I: Basic properties
- Sub-Riemannian geometry
- Volterra series and geometric control theory
- On a generalization of Picard's approximation
- Expansion of solutions of differential systems
- The wave equation on the heisenberg group
- Fonctionnelles causales non linéaires et indéterminées non commutatives
- An expansion formula for differential equations
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