## Abstract

We consider a two-body problem with quick loss of mass which was formulated

by Verhulst in [14]. The corresponding dynamical system is singularly perturbed due to the presence of a small parameter in the governing equations which corresponds to the reciprocal of the initial rate of loss of mass, resulting in a boundary layer in the asymptotics. Here, we showcase a geometric approach which allows us to derive asymptotic expansions for the solutions of that problem via a combination of geometric singular perturbation theory [5] and

the desingularisation technique known as \blow-up" [4]. In particular, we justify the unexpected dependence of those expansions on fractional powers of the singular perturbation parameter; oreover, we show that the occurrence of logarithmic (\switchback") terms therein is due to a resonance phenomenon that arises in one of the coordinate charts after blow-up.

by Verhulst in [14]. The corresponding dynamical system is singularly perturbed due to the presence of a small parameter in the governing equations which corresponds to the reciprocal of the initial rate of loss of mass, resulting in a boundary layer in the asymptotics. Here, we showcase a geometric approach which allows us to derive asymptotic expansions for the solutions of that problem via a combination of geometric singular perturbation theory [5] and

the desingularisation technique known as \blow-up" [4]. In particular, we justify the unexpected dependence of those expansions on fractional powers of the singular perturbation parameter; oreover, we show that the occurrence of logarithmic (\switchback") terms therein is due to a resonance phenomenon that arises in one of the coordinate charts after blow-up.

Original language | English |
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Number of pages | 24 |

Journal | Nonlinear dynamics |

Publication status | Accepted/In press - 4 Jan 2021 |