CONFLUENCE OF SINGULAR POINTS OF ORDINARY DIFFERENTIAL EQUATIONS OF FUCHSIAN TYPE INDUCED BY DEFORMATION OF TWO-DIMENSIONAL HYPERBOLIC CONE-MANIFOLD STRUCTURES

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概要

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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 system $ E_t $ of ordinary differential equations with singular points which depends on the Riemannian metric $ \sigma_t $. If $ t \neq 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.

著者

• FUJII Michihiko

  Department of Mathematics Graduate School of Science Kyoto University

関連論文

• CONFLUENCE OF SINGULAR POINTS OF ORDINARY DIFFERENTIAL EQUATIONS OF FUCHSIAN TYPE INDUCED BY DEFORMATION OF TWO-DIMENSIONAL HYPERBOLIC CONE-MANIFOLD STRUCTURES

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