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Let $ { sigma_t }_t in (-infty, infty) $ be a one-parameter family of hyperbolic Riemannian metrics on an open annulus which is continuouswith respect to the Gromov-Hausdorff topology. We consider a s...ystem $ E_t $ of ordinary differential equations with singular points which depends on the Riemannian metric $ sigma_t $. If $ t \eq 0 $, all of the singular points of $ E_t $ are regular. If $ t = 0 $, $ E_0 $ has an irregular singular point. In this paper, we investigate the behavior of the singular points of $ E_t $. We show that a regular singular point of $ E_t $, together with another regular singular point of $ E_t $, becomes the irregular singular point of $ E_0 $ as $ t $ $ (>0) $ tends to zero and that the irregular singular point of $ E_0 $ becomes a non-singular point of $ E_t $ as $ t $ decreases from zero.続きを見る
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Mendeley出力
