Geometry and analysis of analytic vector fields

解析向量场的几何和分析

• 批准号: 8528-2010
• 负责人: Schlomiuk, Dana
• 金额: $ 0.87万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=474403
• 关键词: Geometry; analysis; analytic; vector; fields

Planar polynomial or analytic differential systems are ubiquitous in applications and they are also of theoretical importance. There are several hard problems on such systems which have remained unsolved for more than a century: two famous problems posed by Poincar\'e and one posed by Hilbert, the second part of his 16th problem. The proposal will throw light on these deep longstanding questions.

平面多项式或平面解析微分系统在实际应用中是普遍存在的，也具有重要的理论意义。关于这类系统，有几个难题在世纪以来一直没有得到解决：庞加莱提出的两个著名问题和希尔伯特提出的第16个问题的第二部分。该提案将有助于阐明这些长期存在的深层次问题。