عنوان

Global transversality, resonance and chaotic dynamics /

شابک

1281911682

شابک

6611911685

شابک

9781281911681

شابک

9786611911683

شابک

9789812771124

شابک

9812771123

شابک اشتباه

9789812771117

شابک اشتباه

9812771115

شماره

b787284

عنوان اصلي

Global transversality, resonance and chaotic dynamics /

نام عام مواد

[Book]

نام نخستين پديدآور

Albert C.J. Luo.

محل نشرو پخش و غیره

Hackensack, NJ :

نام ناشر، پخش کننده و غيره

World Scientific,

تاریخ نشرو بخش و غیره

©2008.

نام خاص و کميت اثر

1 online resource (xii, 447 pages) :

ساير جزييات

illustrations (some color)

متن يادداشت

Includes bibliographical references (pages 437-444) and index.

متن يادداشت

Ch. 1. Introduction. 1.1. A brief history of dynamics. 1.2. Nonlinear Hamiltonian systems. 1.3. Dissipative nonlinear systems. 1.4. Book layout -- ch. 2. Differential geometry of flows. 2.1. Normal distance and G-functions. 2.2. Non-contact flows. 2.3. Contact flows. 2.4. Concluding remarks -- ch. 3. Global transversality in continuous dynamical systems. 3.1. Nonlinear dynamical systems. 3.2. Local and global flows. 3.3. Global transversality. 3.4. Global tangency. 3.5. Perturbed Hamiltonian systems. 3.6. Two-dimensional Hamiltonian systems. 3.7. A damped Duffing oscillator. 3.8. Global transversality to a generalized separatrix -- ch. 4. Chaotic layer dynamics. 4.1. Chaotic domains in phase space. 4.2. First integral quantity increments. 4.3. Resonance mechanism of chaotic layers. 4.4. Energy increments in perturbed Hamiltonian systems -- ch. 5. Two-dimensional stochastic layers. 5.1. Geometric description in phase space. 5.2. Approximate predictions. 5.3. Stochastic layer in a Duffing oscillator. 5.4. Conclusions and discussions -- ch. 6. Stochasticity in resonant separatrix layers. 6.1. Two-dimensional resonant separatrix layers. 6.2. 2n-dimensional resonant separatrix layers. 6.3. Resonant layers in a Duffing oscillator. 6.4. Resonant layers in a parametric pendulum -- ch. 7. Nonlinear dynamics on an equi-energy surface. 7.1. Hamiltonian systems. 7.2. Nonlinear resonance. 7.3. Energy spectrum. 7.4. Chaotic motions on an equi-energy surface. 7.5. Conclusions -- ch. 8. Stability and grazing in dissipative systems. 8.1. Equilibrium stability. 8.2. Periodic flow stability. 8.3. Local grazing bifurcation. 8.4. Global grazing bifurcation -- ch. 9. Global dynamics in two-dimensional dynamical systems. 9.1. Tangency and transversality. 9.2. Energy increment and Melnikov function. 9.3. Mapping structures. 9.4. Bifurcation scenario. 9.5. Numerical illustrations -- ch. 10. Flow switchability in discontinuous dynamical systems. 10.1. Discontinuous dynamical systems. 10.2. Passable flows. 10.3. Non-passable flows. 10.4. Tangential flows. 10.5. Flow switching bifurcations. 10.6. First integral quantity increment.

بدون عنوان

0

متن يادداشت

This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n-dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in nonlinear dynamics.

عنوان

Global transversality, resonance and chaotic dynamics.

شماره استاندارد بين المللي کتاب و موسيقي

9789812771117

موضوع مستند نشده

Chaotic behavior in systems.

موضوع مستند نشده

Dynamics.

موضوع مستند نشده

Nonlinear systems.

موضوع مستند نشده

Chaotic behavior in systems.

موضوع مستند نشده

Dynamics.

موضوع مستند نشده

Nonlinear systems.

موضوع مستند نشده

SCIENCE-- Chaotic Behavior in Systems.

موضوع مستند نشده

PBWR

موضوع مستند نشده

PBWR

موضوع مستند نشده

PBWR

موضوع مستند نشده

SCI-- 012000

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Luo, Albert C. J.

تاريخ عمليات

20201207010055.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y