  In 2019 Anthony Quas, Philippe Thieullen and Mohamed Zarrabi introduced the
concept of strong fast invertibility for linear cocycles. It relates the growth
of volumes between different initial times and, together with a condition on
singular value gaps, yields the existence of a dominated splitting of the
dynamics. The properties of this splitting largely coincide with those for
systems with stable Lyapunov exponents.
  In this article, we take a closer look at strongly fast invertible systems
with bounded coefficients. By linking the dimensions at which a system admits
strong fast invertibility to the multiplicities of Lyapunov exponents, we are
able to give a full characterization of regular strongly fast invertible
systems similar to that of systems with stable Lyapunov exponents. In
particular, we show that the stability of Lyapunov exponents implies strong
fast invertibility (even in the absence of regularity). Central to our
arguments are certain induced systems on spaces of exterior products that
represent the evolution of volumes.
  Finally, we derive convergence results for the computation of Lyapunov
exponents via Benettin's algorithm using perturbation theory. While the
stronger assumption of stable Lyapunov exponents clearly leaves more freedom on
how to choose stepsizes, we derive conditions for the stepsizes with which
convergence can be ensured even if a system is only strongly fast invertible.
