  We study the problem of maintaining a lightweight bounded-degree
$(1+\varepsilon)$-spanner of a dynamic point set in a $d$-dimensional Euclidean
space, where $\varepsilon>0$ and $d$ are arbitrary constants. In our
fully-dynamic setting, points are allowed to be inserted as well as deleted,
and our objective is to maintain a $(1+\varepsilon)$-spanner that has constant
bounds on its maximum degree and its lightness (the ratio of its weight to that
of the minimum spanning tree), while minimizing the recourse, which is the
number of edges added or removed by each point insertion or deletion. We
present a fully-dynamic algorithm that handles point insertion with amortized
constant recourse and point deletion with amortized $O(\log\Delta)$ recourse,
where $\Delta$ is the aspect ratio of the point set.
