4． Bifurcations of Limit Cycles for a Pair of Multipliers Crossing the
Unit Circle at±i
4．1． Degenerate Families
4．2． Degenerate Families Found Analytically
4．3． Degenerate Families Found Numerically
4．4． Bifurcations iNondegenerate Families
4．5． Limit Cycles of Systems with a Fourth Order Symmetry
5． Finitely-Smooth Normal Forms of Local Families
5．1． A Synopsis of Results
5．2． Definitions and Examples
5．3． General Theorems and Deformations of Nonresonant Germs
5．4． Reductioto Linear Normal Form
5．5． Deformations of Germs of Diffeomorphisms of Poincare Type
5．6． Deformations of Simply Resonant Hyperbolic Germs
5．7． Deformations of Germs of Vector Fields with One Zero Eigenvalue at a Singular Point
5．8． Functional Invariants of Diffeomorphisms of the Line
5．9． Functional Invariants of Local Families of Diffeomorphisms
5．10． Functional Invariants of Families of Vector Fields
5．11． Functional Invariants of Topological Classifications of Local Families of Diffeomorphisms of the Line
6． Feigenbaum Universality for Diffeomorphisms and Flows
6．1． Period-Doubling Cascades
6．2． Perestroikas of Fixed Points
6．3． Cascades of n-fold Increases of Period
6．4． Doubling iHamiltoniaSystems
6．5． The Period-Doubling Operator for One-Dimensional Mappings
6．6． The Universal Period-Doubling Mechanism for Diffeomorphisms

Chapter 3． Nonlocal Bifurcations
1． Degeneracies of Codimensio1． Summary of Results
1．1． Local and Nonlocal Bifurcations
1．2． Nonhyperbolic Singular Points
1．3． Nonhyperbolic Cycles
1．4． Nontransversal Intersections of Manifolds
1．5． Contours
1．6． BifurcatioSurfaces
1．7． Characteristics of Bifurcations
1．8． Summary of Results
2． Nonlocal Bifurcations of Flows oTwo-Dimensional Surfaces
2．1． Semilocal Bifurcations of Flows oSurfaces
2．2． Nonlocal Bifurcations oa Sphere： The One-Parameter Case ．
2．3． Generic Families of Vector Fields
2．4． Conditions for Genericity
2．5． One-Parameter Families oSurfaces different from the Sphere
2．6． Global Bifurcations of Systems with a Global Transversal Sectiooa Torus
2．7． Some Global Bifurcations oa Kleibottle
2．8． Bifurcations oa Two-Dimensional Sphere： The Multi-Parameter Case
2．9． Some OpeQuestions
3． Bifurcations of Trajectories Homoclinic to a Nonhyperbolic Singular Point
3．1． A Node iits Hyperbolic Variables
3．2． A Saddle iits Hyperbolic Variables： One Homoclinic Trajectory
3．3． The Topological Bernoulli Automorphism
3．4． A Saddle iits Hyperbolic Variables： Several Homoclinic Trajectories
3．5． Principal Families
4． Bifurcations of Trajectories Homoclinic to a Nonhyperbolic Cycle
4．1． The Structure of a Family of Homoclinic Trajectories
4．2． Critical and Noncritical Cycles
4．3． Creatioof a Smooth Two-Dimensional Attractor
4．4． Creatioof Complex Invariant Sets （The Noncritical Case） ．．．
4．5． The Critical Case
4．6． A Two-Step Transitiofrom Stability to Turbulence
4．7． A Noncompact Set of Homoclinic Trajectories
4．8． Intermittency
4．9． Accessibility and Nonaccessibility
4．10． Stability of Families of Diffeomorphisms
4．11． Some OpeQuestions
5． Hyperbolic Singular Points with Homoclinic Trajectories
5．1． Preliminary Notions： Leading Directions and Saddle Numbers
5．2． Bifurcations of Homoclinic Trajectories of a Saddle that Take Place othe Boundary of the Set of Morse-Smale Systems
5．3． Requirements for Genericity
5，4， Principal Families iR3 and their Properties
5．5． Versality of the Principal Families
5．6． A Saddle with Complex Leading DirectioiR3
5．7． AAddition： Bifurcations of Homoclinic Loops Outside the Boundary of a Set of Morse-Smale Systems
5．8． AAddition： Creatioof a Strange Attractor upoBifurcatioof a Trajectory Homoclinic to a Saddle
6． Bifurcations Related to Nontransversal Intersections
6．1． Vector Fields with No Contours and No Homoclinic Trajectories
6．2． A Theorem oInaccessibility
6．3． Moduli
6．4． Systems with Contours
6．5． Diffeomorphisms with Nontrivial Basic Sets
6．6， Vector Fields iR3 with Trajectories Homoclinic to a Cycle
6．7． Symbolic Dynamics
6．8． Bifurcations of Smale Horseshoes
6．9． Vector Fields oa BifurcatioSurface
6．10． Diffeomorphisms with aInfinite Set of Stable Periodic Trajectories
7． Infinite Nonwandering Sets
7．1． Vector Fields othe Two-Dimensional Torus
7．2． Bifurcations of Systems with Two Homoclinic Curves of a Saddle
7．3． Systems with Feigenbaum Attractors
7．4． Birth of Nonwandering Sets
7．5． Persistence and Smoothness of Invariant Manifolds

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自然科学 数学 数学理论

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