# Gevrey Asymptotic Implicit Function Theorem

@inproceedings{Nikolaev2021GevreyAI, title={Gevrey Asymptotic Implicit Function Theorem}, author={Nikita Nikolaev}, year={2021} }

We prove an Asymptotic Implicit Function Theorem in the setting of Gevrey asymptotics with respect to a parameter. The unique implicitly defined solution admits a Gevrey asymptotic expansion and furthermore it is the Borel resummation of the corresponding implicitly defined formal power series solution. The main theorem can therefore be rephrased as an Implicit Function Theorem for Borel summable power series. As an application, we give a diagonal or Jordan decomposition for holomorphic…

## One Citation

### Exact Perturbative Existence and Uniqueness Theorem

- Mathematics
- 2022

We prove a general existence and uniqueness theorem for holomorphic perturbative solutions of singularly perturbed nonlinear complex differential systems of the form ~∂xf = F (x, ~, f) where ~ is a…

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