Differential Algebraic Methods in Catastrophe Theory: A Rigorous Foundation for Explicit Parameterizations and Singularity Classification

Differential Algebraic Methods in Catastrophe Theory: A Rigorous Foundation for Explicit Parameterizations and Singularity Classification | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 31 October 2025 V1 Latest version Share on Differential Algebraic Methods in Catastrophe Theory: A Rigorous Foundation for Explicit Parameterizations and Singularity Classification Author : shifa liu 0009-0003-6570-2812 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176194051.13606418/v1 163 views 120 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract 本文开发了一个严谨的微分代数框架，用于构建灾变图的显式参数化和灾变理论中的奇点分类。在经典微分代数、代数几何和奇点理论的基础上，我们使用函数场的微分扩展为灾变图构建显式局部参数化。关键创新是系统地使用从切锥和高阶邻域的几何中得出的组合校正项。我们为主要定理提供完整的证明，包括折叠灾变、尖头灾变和燕尾灾变在内的详细示例和完整的验证，并与经典灾变理论建立精确的联系。该框架提供了新的计算工具，同时保持了完整的数学严谨性。我们的方法仅限于特征零域上的不可约代数簇，并且我们仔细解决参数化存在所需的技术条件，特别是微分代数扩展中切锥的合理性和收敛性质。 Supplementary Material File (catastrophe_theory.pdf) Download 385.01 KB Information & Authors Information Version history V1 Version 1 31 October 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords bifurcation analysis catastrophe theory combinatorial corrections differential algebra explicit parameterization singularity classification tangent cones universal unfoldings Authors Affiliations shifa liu 0009-0003-6570-2812 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 163 views 120 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation shifa liu. 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