圆映射PDF电子书下载

第1章 圆映射描述的周期与准周期运动 1

§1 The definition of circle maps 1

Chapter 1 Periodic and quasiperiodic motion described by circle maps 1

§1 圆映射的定义 1

§2 可逆圆映射 5

§2 Invertible circle maps 5

§3 法里树的数论与法里序列的符号表示 10

§3 Number theory of the Farey tree and symbolic representation of the Farey sequence 10

§4 正弦圆映射参数平面上的相结构 16

§4 Phase structure in parametric plan of the sine circle map 16

§5 转数区间、阿诺尔德舌头、双稳和拓扑混沌 19

§5 Rotation intervals，Arnol’d tongues，bistability and topological chaos 19

第2章 圆映射的符号动力学 23

§6 周期轨道的符号表示 23

§6 Symbolic representation of periodic orbits 23

Chapter 2 Symbolic dynamics of circle maps 23

§7 Symbolic dynamics of Farey sequence 26

§7 法里序列的符号动力学 26

§8 Newborn orbits and theorem for topological degree 29

§8 新生轨道与拓扑度定理 29

§9 The * product of Farey sequence and M．S．S．sequence and the binary tree 32

§9 法里序列与M．S．S．序列的*积及二元树 32

第3章 由准周期向混沌过渡的标度律 36

§10 标度行为的数值研究 36

§10 Numerical research on the scaling behavior 36

Chapter 3 Scaling law for transition from quasiperiod to chaos 36

§11 临界准周期轨道的分形结构 42

§11 Fractal structure of the critical quasiperiodic orbits 42

§12 Renormalization group analysis 46

§12 重正化群分析 47

§13 临界线上转数阶梯标度性质的数值研究 51

§13 Numerical research on the scaling properties of rotation number staircase at critcal line 51

§14 Renormalization group analysis for devil’s staircase 57

§14 关于魔梯的重正化研究 57

§15 圆映射的一般标度性 60

§15 Universal scaling in circle maps 60

§16 超临界圆映射的一般分岔行为 71

Chapter 4 Bifurcation behavior and scaling law of supercritical circle maps 71

§16 General bifurcation behavior of the supercritical circle map 71

第4章 超临界圆映射的分岔行为与标度律 71

§17 The diffusion behavior described by supercritical circle map 74

§17 w＝0超临界圆映射所描述的扩散行为 74

§18 The similarity of the Arnol’d tongues near critical line 78

§18 接近临界线处阿诺尔德舌头的相似性 78

§19 Universal vector scaling of period-doubling bifurcation 81

§19 倍周期分岔的矢量标度律 81

§20 The similarity of the bifurcation in Arnol’d tongues for Fibonacci sequence 88

§20 菲波那契序列阿诺尔德舌头中分岔的相似性 88

§21 Chaotic measures and scaling for supercritical circle map 90

§21 超临界圆映射的混沌测度及其标度律 90

Chapter 5 Examples for circle maps in physical reality 98

§22 Periodically forced damped pendulum，Josephson junction and charge-density wave systems 98

§22 周期驱动阻尼单摆、约瑟夫逊结与电荷密度波系统 98

第5章 实际问题中的圆映射举例 98

§23 Periodically forced Rayleigh-Benard Convective fluid 106

§23 周期强迫瑞利-贝纳德对流系统 106

§24 Global universality in the Frenkel-Kontorova model 109

§24 Frenkel-Kontorova模型中的整体普适性 109

§25 Excitable oscillator under periodic perturbation and rhythm of heartbeat 112

§25 可激振子的周期扰动与心脏的搏动节律 112

§26 Phase locking and chaotic responses of a biological neuron under periodic stimulation 119

§26 神经原对周期脉冲的锁相与混沌响应 119

§27 Integrate-and-fire models and the transitiib from quasiperiodicity to nonchaotic complete phase locking 125

§27 累积-释放模型与由准周期至完全锁相的非混沌转变 125

§28 Complete phase locking and chaos in modulated relaxation oscillators 129

§28 调制弛豫振子的完全锁相与混沌 129

Chaper 6 Torus maps 137

§29 Torus maps and resonance regions 137

§29 环面映射及其共振区 137

第6章 环面映射 137

§30 Numerical experiments on N-frequency quasiperiodicity 142

§30 关于环面映射的数值实验 142

§31 Three frequency competing in a nonlinear electronic oscillator circuit 149

§31 一个非线性电子振荡线路中的三频问题 149

§32 Renormalization group analysis for three frequency quasiperod 151

§32 三频问题的重正化群分析 151

§33 The quasiperiodically forced circle map 157

§33 准周期强迫圆映射 157

§34 Identification and experrimental observation for a strange nonchaotic attractor 163

§34 非混沌奇怪吸引子的鉴别与实验观测 163

Refefences 169

参考文献 169