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Titlebook: Integrability of Dynamical Systems: Algebra and Analysis; Xiang Zhang Book 2017 Springer Nature Singapore Pte Ltd. 2017 integrability.Jaco

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发表于 2025-3-21 19:42:09 | 显示全部楼层 |阅读模式
书目名称Integrability of Dynamical Systems: Algebra and Analysis
编辑Xiang Zhang
视频videohttp://file.papertrans.cn/469/468274/468274.mp4
概述Equips the reader with an understanding of integrability.Summarizes the classical results of Darboux integrability and its modern development.Connects analysis, algebraic geometry, field extension, di
丛书名称Developments in Mathematics
图书封面Titlebook: Integrability of Dynamical Systems: Algebra and Analysis;  Xiang Zhang Book 2017 Springer Nature Singapore Pte Ltd. 2017 integrability.Jaco
描述.This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on the Darboux theory of integrability and local integrability together with their applications. It summarizes the classical results of Darboux integrability and its modern development together with their related Darboux polynomials and their applications in the reduction of Liouville and elementary integrabilty and in the center—focus problem, the weakened Hilbert 16th problem on algebraic limit cycles and the global dynamical analysis of some realistic models in fields such as physics, mechanics and biology.. .Although it can be used as a textbook for graduate students in dynamical systems, it is intended as supplementary reading for graduate students from mathematics, physics, mechanics and engineering in courses related to the qualitative theory, bifurcation theory and the theory of integrability of dynamical systems..
出版日期Book 2017
关键词integrability; Jacobian multipliers; Darboux integrability; Liouvillian integrability; Darboux polynomi
版次1
doihttps://doi.org/10.1007/978-981-10-4226-3
isbn_softcover978-981-13-5082-5
isbn_ebook978-981-10-4226-3Series ISSN 1389-2177 Series E-ISSN 2197-795X
issn_series 1389-2177
copyrightSpringer Nature Singapore Pte Ltd. 2017
The information of publication is updating

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发表于 2025-3-21 21:41:14 | 显示全部楼层
Local Integrability of Differential Systems,and the existence of analytic normalizations of analytic integrable (or partially integrable) differential systems. We will also introduce the local theory of Darboux integrability of local analytic or formal differential systems.
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The Fundamentals of the Theory of Integrability of Differential Systems,in the canonical regions. As a preliminary application of the integrability theory, we use it to solve linear and quasilinear partial differential equations. Lastly, we introduce a few fundamental results on Lax pairs for finding the first integrals of ordinary differential equations.
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Algebraic, Analytic and Meromorphic Integrability,ian systems, and the meromorphic integrability of differential systems near a given orbit via the differential Galois group. Finally, we present an algorithm to compute the rational first integrals and the Darboux polynomials of polynomial differential systems.
发表于 2025-3-22 23:10:06 | 显示全部楼层
Applications of the Darboux Theory of Integrability, the center-focus and the limit cycle problems of planar polynomial differential systems. In the last section we will also present applications of this theory to specific models in two and higher dimensions.
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