| 勒让德开折及其生成族 |
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| 引用本文： | 孙伟志,许静波.勒让德开折及其生成族[J].吉林师范大学学报（自然科学版）,2014(4):6-10. |
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| 作者姓名： | 孙伟志 许静波 |
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| 作者单位： | 1. 东北师范大学 人文学院,吉林 长春,130117
2. 吉林师范大学 数学学院 吉林 四平 136000 |
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| 基金项目： | 国家自然科学基金项目(11301215，10871035)；吉林省自然科学基金项目(20130522094JH)；吉林省教育厅“十二五”科学技术研究项目 |
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| 摘 要： | 本文给出1-参数勒让德开折与多重勒让德开折的定义并讨论它们的生成族的构造,证得多重函数芽的K-余维估计定理,该结果是对克莱罗型微分方程与完全可积一阶偏微分方程几何奇点进行半局部分类的基础.
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| 关 键 词： | 1-参数勒让德开折 多重勒让德开折 生成族 多重函数芽 余维估计 |
Legendrian Unfoldings and Its Generating Families |
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| SUN Wei-zhi,XU Jing-bo.Legendrian Unfoldings and Its Generating Families[J].Jilin Normal University Journal(Natural Science Edition),2014(4):6-10. |
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| Authors: | SUN Wei-zhi XU Jing-bo |
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| Institution: | SUN Wei-zhi, XU Jing-bo ( 1. College of Humanities and Sciences, Northeast Normal University, Changchun 130117, China; 2. College of Mathematics, Jilin Normal University, Siping 136000, China) |
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| Abstract: | The notions of one-parameter Legendrian unfolding and multi-Legendrian unfolding are given,and the structures of their generating families are studied. The theorem of estimate of codimensions for multi-germs under K-equivalence is proved. The results are the basis of semi-local classification of geometric singulatities for the differential equations of Clairaut type and completely integrable holonomic systems of first-order differential equations. |
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| Keywords: | one-parameter Legendrian unfolding multi-Legendrian unfolding multi-germ estimate of codimen-sions |
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