# Flatness of invariant manifolds for stochastic partial differential equations driven by L\'{e}vy processes

## TL;DR

This paper proves that the flatness of invariant manifolds in certain stochastic PDEs driven by Lévy processes is at least equal to the number of sources with small jumps, supported by an illustrative example.

## Contribution

It establishes a lower bound on the flatness of invariant manifolds for stochastic PDEs driven by Lévy processes, linking it to the number of small jump sources.

## Key findings

- Flatness is at least equal to the number of small jump sources.
- Provides an example illustrating the theoretical result.

## Abstract

The purpose of this note is to prove that the flatness of an invariant manifold for a semilinear stochastic partial differential equation driven by L\'{e}vy processes is at least equal to the number of driving sources with small jumps. We illustrate our findings by means of an example.