  This paper explores the use of the Approximation of Isolated Resonance (AIR)
method for determining the safe basins (SBs) in the problem of escape from a
potential well. The study introduces a novel approach to capture the location
and the shape of the SBs and establish their erosion profiles. The research
highlights the concept of "true" safe basins, which remain invariant with phase
shifts, a critical factor often faced in real-world applications. A cubic
polynomial potential serves as the benchmark to illustrate the proposed method.
