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A t-spanner is a graph on a set of points Swith the following property: Between any pair of points there is a path in the spanner whose total length is at most ttimes the actual distance between the points. In this paper, we consider points residing in a metric space equipped with doubling dimension 茂戮驴, and show how to construct a dynamic (1 + 茂戮驴)-spanner with degree 茂戮驴茂戮驴 O(茂戮驴)in $O(\frac{\log n}{\varepsilon^{O(\lambda)}})$ update time. When 茂戮驴and 茂戮驴are taken as constants, the degree and update times are optimal.