  Considering stationary states of continuous-variable systems undergoing an
open dynamics, we unveil the connection between properties and symmetries of
the latter and the dynamical parameters. In particular, we explore the relation
between the Lyapunov equation for dynamical systems and the steady-state
solutions of a time-independent Lindblad master equation for bosonic modes.
Exploiting bona-fide relations that characterize some genuine quantum
properties (entanglement, classicality, and steerability), we obtain conditions
on the dynamical parameters for which the system is driven to a steady-state
possessing such properties. We also develop a method to capture the symmetries
of a steady state based on symmetries of the Lyapunov equation. All the results
and examples can be useful for steady-state engineering process.
