分歧理论和突变理论-动力系统-V 本书特色

Both bifurcatiotheory and catastrophe theory are studies of smooth systems，tbcusing oproperties that seem manifestly non-smooth. Bifurcations are suddechanges that occur ia system as one or more parameters are varied.Catastrophe theory is accurately described as singularity theory and its applications.
　　These two theories are important tools ithe study of differential equations and of related physical systems.Analyzing the bifurcations or singularities of a system provides useful qualitative informatioabout its behaviour. The authors have writtethis book with reffeshing clarity.Theexpositiois masterful，with penetrating insights.

分歧理论和突变理论-动力系统-V 内容简介

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分歧理论和突变理论-动力系统-V 目录

Preface

Chapter 1． Bifurcations of Equilibria
1． Families and Deformations
1．1． Families of Vector Fields
1．2． The Space of Jets
1．3． Sard's Lemma and Transversality Theorems
1．4． Simplest Applications： Singular Points of Generic Vector Fields
1．5． Topologically Versal Deformations
1．6． The ReductioTheorem
1．7． Generic and Principal Families
2． Bifurcations of Singular Points iGeneric One-Parameter Families
2．1 Typical Germs and Principal Families
2．2． Soft and Hard Loss of Stability
3． Bifurcations of Singular Points iGeneric Multi-Parameter Families with Simply Degenerate Linear Parts
3．1． Principal Families
3．2． BifurcatioDiagrams of the Principal Families （3- ） iTable 1
3．3． BifurcatioDiagrams with Respect to Weak Equivalence and Phase Portraits of the Principal Families （4- ） iTable 1
4． Bifurcations of Singular Points of Vector Fields with a Doubly-Degenerate Linear Part
4．1． A List of Degeneracies
4．2． Two Zero Eigenvalues
4．3． Reductions to Two-Dimensional Systems
4．4． One Zero and a Pair of Purely Imaginary Eigenvalues
4．5． Two Purely Imaginary Pairs
4．6． Principal Deformations of Equations of Difficult Type iProblems with Two Pairs of Purely Imaginary Eigenvalues （Following Zolitdek）
5． The Exponents of Soft and Hard Loss of Stability
5．1． Definitions
5．2． Table of Exponents

Chapter 2． Bifurcations of Limit Cycles
1． Bifurcations of Limit Cycles iGeneric One-Parameter Families
1．1． Multiplier I
1．2． Multiplier-1 and Period-Doubling Bifurcations
1．3． A Pair of Complex Conjugate Multipliers
1．4． Nonlocal Bifurcations iOne-Parameter Families of Diffeomorphisms
1．5． Nonlocal Bifurcations of Periodic Solutions
1．6． Bifurcations Resulting iDestructions of Invariant Tori
2． Bifurcations of Cycles iGeneric Two-Parameter Families with an
Additional Simple Degeneracy
2．1． A List of Degeneracies
2．2． A Multiplier 1or-1 with Additional Degeneracy ithe Nonlinear Terms
2．3． A Pair of Multipliers othe Unit Circle with Additional Degeneracy ithe Nonlinear Terms
3． Bifurcations of Cycles iGeneric Two-Parameter Families with Strong Resonances of Orders q≠4
3．1． The Normal Form ithe Case of Unipotent JordaBlocks
3．2． Averaging ithe Seifert and the M6bius Foliations
3．3． Principal Vector Fields and their Deformations
3．4． Versality of Principal Deformations
3．5． Bifurcations of Stationary Solutions of Periodic Differential Equations with Strong Resonances of Orders q≠4

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自然科学 数学 数学理论

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