《非線性物理科學(xué)：連續(xù)動力系統(tǒng)（英文版）》極具創(chuàng)新特色，首次揭示了混沌不只是可以通過數(shù)字模擬實現(xiàn)，而且可以用解析形式來表示。書中提出了關(guān)于連續(xù)動力系統(tǒng)的穩(wěn)定性和分叉理論的一種新的、清晰簡明的觀點，能夠幫助讀者更好地理解動力系統(tǒng)中的規(guī)則性和復(fù)雜性。本書首先介紹了含多重特征根的線性連續(xù)系統(tǒng)的解析解和穩(wěn)定性理論，并詳細討論了非線性連續(xù)動力系統(tǒng)的穩(wěn)定性和奇異性分類，然后系統(tǒng)地討論動力系統(tǒng)從周期解到混沌的解析道路。此外本書還討論了動力系統(tǒng)流對于同宿或異宿軌道分界面的全局橫截性的解析預(yù)測并且給出了非線性哈密頓系統(tǒng)混沌的解析判據(jù)，從而能更好地確定混沌在非線性動力系統(tǒng)中的物理機理。
本書可作為應(yīng)用數(shù)學(xué)、物理、力學(xué)和控制專業(yè)大學(xué)生的教材或參考書，也可供這些領(lǐng)域的教授和研究人員參考。
作者羅朝俊，非線性動力系統(tǒng)和力學(xué)領(lǐng)域國際知名專家，美國南伊利諾伊大學(xué)愛德華分校終身教授，主要研究領(lǐng)域為非線性哈密頓系統(tǒng)混沌、非線性力學(xué)和不連續(xù)動力系統(tǒng)。
Preface
Chapter 1 Linear Systems and Stab
1.1 Linear systems with distinct eigenvalues
1.2 Operator exponentials
1.3 Linear systems with repeated eigenvalues
1.4 Nonhomogeneous linear systems
1.5 Linear systems with periodic coefficients
1.6 Stability and boundary
1.7 Lower-dimensional linear systems
1.7.1 One-dimensional linear systems
1.7.2 Planar linear systems
1.7.3 Three-dimensional linear systems
References
Chapter 2 Stability Switching and Bifurcation
Preface
Chapter 1 Linear Systems and Stab
1.1 Linear systems with distinct eigenvalues
1.2 Operator exponentials
1.3 Linear systems with repeated eigenvalues
1.4 Nonhomogeneous linear systems
1.5 Linear systems with periodic coefficients
1.6 Stability and boundary
1.7 Lower-dimensional linear systems
1.7.1 One-dimensional linear systems
1.7.2 Planar linear systems
1.7.3 Three-dimensional linear systems
References
Chapter 2 Stability Switching and Bifurcation
2.1 Continuous dynamical systems
2.2 Equilibriums and stabilit
2.3 Bifurcation and stability switching
2.3.1 Stability and switching
2.3.2 Bifurcations
2.3.3 Lyapunov functions and stability
References
Chapter 3 Analytical Periodic Flows and Chaos
3.1 Analytical periodic flows
3.1.1 Autonomous nonlinear systems
3.1.2 Periodically forced nonlinear systems
3.2 Nonlinear vibration systems
3.2.1 Free vibration systems
3.2.2 Periodically forced vibration systems
3.3 A periodically forced Duffing oscillator
References
Chapter 4 Global Transversality and Chaos
4.1 Nonlinear dynamical systems
4.2 Local and global flows
4.3 Global transversal
4.4 Global tangency
4.5 Perturbed Hamiltonian systems
4.6 Two-dimensional Hamiltonian systems
4.7 First integral quantity increment
4.8 A damped Duffing oscillator
4.8.1 Conditions for global transversality and tangency
4.8.2 Poincare mapping and mapping structures
4.8.3 Bifurcation scenario
4.8.4 Numericalillustrations
References
Chapter 5 Resonance and Hamiltonian Chaos
5.1 Stochastic layers
5.1.1 Definitions
5.1.2 Approximate criteria
5.2 Resonant separatrix layers
5.2.1 Layer dynamics
5.2.2 Approximate criteria
5.3 A periodically forced Duffing oscillator
5.3.1 Approximate predictions
5.3.2 Numericalillustrations
5.4 Concluding remarks
References
Index
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