Ordinary dichotomy and global linearization
The author finds sufficient conditions for the topological equivalence between the nonautonomous equation \[ x'= A(t)x+ f(t,x)\qquad (x\in\mathbb{R}^n)\tag{1} \] and its linear system \[ x'= A(t)x.\tag{2} \] That means the existence of a homeomorphism \(H(t,\cdot)\) of \(\mathbb{R}^n\) into \(\mathbb{R}^n\) such: (i) \(H(t,x)\to x\) is bounded in \(\mathbb{R}\times \mathbb{R}^n\), (ii) if \(x(t)\) is a solution of (1) then \(H(t,x(t))\) is a solution of (2).
scientific article; zbMATH DE number 5532919