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Let $$\dot{x}=Ax+v_r(x)+v_{r+1}(x)+ \dots$$ with $x \in \mathbb{C}^n$ and $v_r: \mathbb{C}^n \to \mathbb{C}^n$ a homogenous, polynomial function of order $r.$ Then, being able to find a suitable $h$ ...

Let $A$ be a commutative ring. For an odd positive integer $q$ and an integer $p$ in the range $1 \leq p \leq q$, consider the cochain complex: $0 \to \Lambda^p(A^N) \to \Lambda^{p+q}(A^N) \to \cdots \...