《非线性动力系统和混沌应用导论(第2版)(英文)》的**讲述大量的技巧和观点，包括了深层次学习本科目的**的核心知识，这些可以使学生能够学习特殊动力系统并获得学习这些系统大量信息。因此，像工程、物理、化学和生物专业读者不需要另外学习大量的预备知识。新的版本中包括了大量有关不变流形理论和规范模的新材料，拉格朗日、哈密尔顿、梯度和可逆动力系统的也有讨论，也包括了哈密尔顿分叉和环映射的基本性质。书中附了丰富的参考资料和详细的术语表，使得《非线性动力系统和混沌应用导论(第2版)(英文)》的可读性更加增大。

维金斯编著的《非线性动力系统和混沌应用导论(第2版)(英文)》的**讲述大量的技巧和观点,包括了深层次学习本科目的**的核心知识,这些可以使学生能够学习特殊动力系统并获得学习这些系统大量信息。因此,像工程、物理、化学和生物专业读者不需要另外学习大量的预备知识。新的版本中包括了大量有关不变流形理论和规范模的新材料,拉格朗日、哈密尔顿、梯度和可逆动力系统的也有讨论,也包括了哈密尔顿分叉和环映射的基本性质。书中附了丰富的参考资料和详细的术语表,使得《非线性动力系统和混沌应用导论(第2版)(英文)》的可读性更加增大。

series preface
preface to the second edition
introduction
1 equilibrium solutions，stability,and linearized stability
1.1 equilibria of vector fields
1.2 stability of trajectories
1.2a linearization
1.3 maps。
1.3a definitions of stability for maps
1.3b stability of fixed points of linear maps
1.3c stability of fixed points of maps via the linear approximation
1.4 some terminology associated with fixed points
1.5 application to the unforced duffing oscillator
1.6 exercises
2 liapunov functions series preface preface to the second edition introduction 1 equilibrium solutions，stability,and linearized stability 1.1 equilibria of vector fields 1.2 stability of trajectories 1.2a linearization 1.3 maps。 1.3a definitions of stability for maps 1.3b stability of fixed points of linear maps 1.3c stability of fixed points of maps via the linear approximation 1.4 some terminology associated with fixed points 1.5 application to the unforced duffing oscillator 1.6 exercises 2 liapunov functions 2.1 exercises 3 invariant manifolds：linear and nonlinear systems 3.1 stable，unstable，and center subspaces of linear，autonomous vector fields 3.1a invariance of the stable，unstable，and center subspaces 3.1b some examples. 3.2 stable，unstable，and center manifolds for fixed points of nonlinear，autonomous vector fields 3.2a invariance of the graph of a function：tangency of the vector field to the graph 3.3 maps 3.4 some examples 3.5 existence of invariant manifolds：the main methods of proof,and how they wbrk 3：5a application of these two methods to a concrete example：existence of the unstable manifold 3.6 time-dependent hyperbolic trajectories and their stable and unstable manifoids 3.6a hyperbolic trajectories 3.6b stable and unstable manifolds of hyperbolic trajectories 3.7 invariant manifolds in a broader context 3.8 exercises 4 periodic orbits 4.1 nonexistence of periodic orbits for two-dimensional，autonomous vector fields 4.2 further remarks on periodic orbits 4.3 exercises 5 vector fields possessing an integral 5.1 vector fields on two-manifolds having an integral 5.2 two degree-of-freedom hamiltonian systems and geometry 5.2a dynamics on the energy surface. 5.2b dynamics on an individual torus 5.3 exercises 6 index theory 6.1 exercises 7 some general properties of vector fields： existence，uniqueness，differentiability,and flows 7.1 existence，uniqueness，differentiability with respect to initial conditions 7.2 continuation of solutions 7.3 differentiability with respect to parameters 7.4 autonomous vector fields 7.5 nonautonomous vector fields 7.5a the skew—product flow approach 7.5b the cocycle approach 7.5c dynamics generated by a bi—infinite sequence of maps 7.6 liouville's theorem 7.6a volume preserving vector fields and the poincar6 recurrence theorem 7.7 exercises 8 asymptotic behavior 8.1the asymptotic behavior oftrajectories. 8.2 attracting sets，attractors.and basins of attraction 8.3 the lasalle invariance principle 8.4 attraction in nonautonomous systems 8.5 exercises 9 the poinear6-bendixson theorem 9.1 exercises 10 poinear6 maps 10.1 cuse 1：poincar6 map near a periodic orbit 10.2 case 2：the poincar6 map of a time-periodic ordinary differential equation 10.2a periodically forced linear oscillators 10.3 case 3：the poincar6 mad near a homoclinic orbit 10.4 case 4：poincar6 map associated with a two degree-of-freedom hamiltonian system 10.4a the study of coupled oscillators via circle maps 10.5 exercises 11 conjugacies of maps，and varying the cross.section 11.1 case 1：poincar6 map near a periodic orbit：variation of the cross—section 11.2 case 2：the poincard map of a time-periodic ordinary differential equation：variation of the cross—section 12 structural stability，genericity，and transversality 12.1 definitions of structural stability and genericity。 12.2 transversality 12.3 exercises。。 13 lagrange's equations 13.1 generalized coordinates 13.2 derivation of lagrange's equations 13.2a the kinetic energy 13.3 the energy integral 13.4 momentum integrals 13.5 hamilton's equations 13.6 cyclic coordinates.routh's equations.and reduction of the number of equations 13.7 variational methods 13.7a the principle of least action 13.7b the action principle in phase space。 13.7c transformations that preserve the form of hamilton's equations 13.7d applications of variational methods 13.8 the hamilton.jacobi equation 13.8a applications of the hamilton—jacobi equation 13.9 exercises， 14 hamiltonian vector fields 14.1 symplectic forms 14.1a the relationship between hamilton's equations and the symplectic form 14.2 poisson brackets 14.2a hamilton’s equations in poisson bracket form 14.3 symplectic or canonical transformations. 14.3a eigenvalues of symplectic matrices 14.3b infinitesimally symplectic transformations 14.3c the eigenvalues of infinitesimally symplectic matrices 14.3d the flow generated by hamiltonian vector fields is a one-parameter famiiy of symplectic transformations 14.4 transformation of hamilton's equations under symplectic transformations 14.4a hamilton's equations in complex coordinates 14.5 completely integrable hamiltonian systems 14.6 dynamics of completely integrable hamiltonian systems in action—angle coordinates 14.6a resonance and nonresonance 14.6b diophantine frequencies 14.6c geometry of the resonances 14.7 perturbations of completely integrable hamiltonian systems in action-angle coordinates 14.8 stability of elliptic equilibria 14.9 discrete-time hamiltonian dynamical systems：iteration of symplectic maps 14.9a the kam theorem and nekhoroshev's theorem for symplectic maps. 14.10 genetic properties of hamiltonian dynamical systems 14.11 exercises 15 gradient vector fields 15.1 exercises 16 reversible dynamical systems 16.1 the definition of reversible dynamical systems 16.2 examples of reversible dynamical systems 16.3 linearization of reversible dynamical systems 16.3a continuous time 16.3b discrete time …… 17 asymptotically autonomous vector fields 18 center manifolds 19 normal forms 20 bifurcation of fixed points of vector fields 21 bifurcations of fixed points of maps 23 the smale horseshoe 24 symbolic dynamics 25 the conley-moser conditions，or“how to prove that a dynamical system is chaotic” 26 dynamics near homoclinic points oftwo-dimensional maps 27 orbits homoclinic to hyperbolic fixed points in three-dimensional autonomous v.ector fields 28 melnikov's method for homoclinic orbits in two-dimensional，time-periodic vector fields 29 liapunov exponents 30 chaos and strange attractors 31 hyperbolic invariant sets：a chaotic saddle 32 long period sinks in dissipative systems and elliptic islands in conservative systems 33 global bifurcations arising from local codimension--two bifurcations 34 glossary of frequently used terms bibliography index

维金斯编著的《非线性动力系统和混沌应用导论(第2版)(英文)》的**讲述大量的技巧和观点,包括了深层次学习本科目的**的核心知识,这些可以使学生能够学习特殊动力系统并获得学习这些系统大量信息。因此,像工程、物理、化学和生物专业读者不需要另外学习大量的预备知识。新的版本中包括了大量有关不变流形理论和规范模的新材料,拉格朗日、哈密尔顿、梯度和可逆动力系统的也有讨论,也包括了哈密尔顿分叉和环映射的基本性质。书中附了丰富的参考资料和详细的术语表,使得《非线性动力系统和混沌应用导论(第2版)(英文)》的可读性更加增大。