二阶非线性系统的奇点量、中心问题与极限环分叉

出版时间：2007-12  出版社：科学  作者：本社  页数：228  

内容概要

近年来，非线性动力学理论和方法正从低维向高维乃至无穷维发展。伴随着计算机代数、数值模拟和图形技术的进步，非线性动力学所处理的问题规模和难度不断提高。　　本套丛书在选题和内容上有别于于郝柏林先生主编的《非先行科学丛书》它更加侧重于对工程科学，生命科学，社会科学等领域中的非先行动力学问题进行建模，理论分析，计算和实验。与国外的同类丛书相比，它更具有整体的出版思想，每分册阐述一个主题，互不重复等特点。丛书的选题主要来自我过学者在国家自然科学基金等资助的研究成果，有些研究成果已别国内外学者广泛引用或应用与工程和社会实践，还有一些选题取自作者多年的教学成果。

书籍目录

Chapter 1  Focal Values, Saddle Values and Singular Point Values  1.1  Successor Functions and Properties of Focal Values  1.2  Poincare Formal Series and Algebraic Equivalence  1.3  Singular Point Values and Conditions of Integrability  1.4  Linear Recursive Formulas for the Computation of Singular Point Values  1.5  The Algebraic Construction of Singular Values  1.6  Elementary Invariants of the Cubic Systems  1.7  Singular Point Values of the Quadratic Systems and the Homogeneous Cubic SystemsChapter 2  Theory of Center-focus for a Class of Infinite Singular Points and Higher-order Singular Points  2.1  Conversion of the Questions  2.2  Theory of Center-focus at the Infinity for a Class of Systems   2.3  Theory of Center-focus of Higher-order Singular Points for a Class of Systems  2.4  The Construction of Singular Point Values of Higher-order Singular Points and Infinity  2.5  Translational Invariance of the Singular Values at InfinityChapter 3  Multiple Hopf Bifurcations  3.1  The Zeros of Successor Functions in the Polar Coordinates  3.2  Analytic Equivalence  3.3  Weak Bifurcation Function Some Polynomial Vector Fields  4.1  Cubic Systems Created Four Limit Cycles at Infinity  4.2  Cubic Systems Created Seven Limit Cycles at InfinityChapter 5  Local and Non-local Bifurcations of Perturbed Zq-equivatiant Hamiltonian Vector Fields  5.1  Zq-equivariant Planar Vector Fields and an Example　5.2  The Method of Detection Functions: Rough Perturbations of Zp- equivariant Hamiltonian Vector Fields　5.3  Bifurcations of Limit Cycles of a Z2- equivariant Perturbed Hamiltonian Vector Fields　5.4  The Rate of Growth of Hilbert Number H(n) with nChapter 6  Isochronous Center  6.1  Isochronous Centers and Period Constants  6.2  Complex Period Constants  6.3  Application of the Method of Section 6.2  6.4  The Method of Time-angle Difference  6.5  Conditions of Isochronous Center for a Cubic System  6.6  Isochronous Centers at Infinity of Polynomial SystemsChapter 7  On Quasi Analytic Systems  7.1  Preliminary  7.2  Reduction of the Problems  7.3  Focal Values, Periodic Constants and First Integrals of (7.2.3)  7.4  Singular Point Values and Bifurcations of Limit Cycles of Quasi-quadratic Systems  7.5  Integrability of Quasi-quadratic Systems  7.6  Node Point Values　7.7  Isochronous Center of Quasi-quadratic SystemsChapter 8  Complete Study on a Bi-center Problem for the Z2-equivariant Cubic Vector Fields　8.1  Introduction and Main Results　8.2  The Reduction of System Having Two Elementary Focuses at (1,0) and (-1,0)　8.3  Lyapunov Constants. Invariant Integrals and the Necessary and Sufficient Conditions of the Existence for the Bi-center　8.4  The Conditions of Six-order Fine Focus of (8.3.2) and Bifurcations of Limit CyclesBibliography

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