二階非線性系統(tǒng)的奇點量、中心問題與極限環(huán)分叉

內(nèi)容概要

近年來，非線性動力學(xué)理論和方法正從低維向高維乃至無窮維發(fā)展。伴隨著計算機(jī)代數(shù)、數(shù)值模擬和圖形技術(shù)的進(jìn)步，非線性動力學(xué)所處理的問題規(guī)模和難度不斷提高?！　”咎讌矔谶x題和內(nèi)容上有別于于郝柏林先生主編的《非先行科學(xué)叢書》它更加側(cè)重于對工程科學(xué)，生命科學(xué)，社會科學(xué)等領(lǐng)域中的非先行動力學(xué)問題進(jìn)行建模，理論分析，計算和實驗。與國外的同類叢書相比，它更具有整體的出版思想，每分冊闡述一個主題，互不重復(fù)等特點。叢書的選題主要來自我過學(xué)者在國家自然科學(xué)基金等資助的研究成果，有些研究成果已別國內(nèi)外學(xué)者廣泛引用或應(yīng)用與工程和社會實踐，還有一些選題取自作者多年的教學(xué)成果。

書籍目錄

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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