Maximal linear transformation groups preserving asymptotic properties of linear differential systems. I (Q1935416)

The paper deals with linear differential systems \[ \dot{x}=A(t)x,\quad x\in \mathbb{R}^n,\;t\geq 0\tag{1} \] with piecewise-continuous matrix \(A\). The problem of describing sets of linear transformations \(x=L(t)y\) with a piecewise-differentiable matrix \(L\) that preserves some asymptotic properties of linear systems is considered. In particular, the set of linear transformations preserving the property of boundedness of the coefficients of (1) is described.