Methods of Qualitative Theory in Nonlinear Dynamics,9789810233822

Methods of Qualitative Theory in Nonlinear Dynamics

by ; ; ;
ISBN13: 9789810233822
ISBN10: 9810233825
Format: Hardcover
Pub. Date: 1998-06-01
Publisher(s): WORLD SCIENTIFIC PUB CO INC
  • eCampus.com Device Compatibility Matrix

    Click the device icon to install or view instructions

    Apple iOS | iPad, iPhone, iPod
    Apple iOS | iPad, iPhone, iPod
    Android Devices | Android Tables & Phones OS 2.2 or higher | *Kindle Fire
    Android Devices | Android Tables & Phones OS 2.2 or higher | *Kindle Fire
    Windows 10 / 8 / 7 / Vista / XP
    Windows 10 / 8 / 7 / Vista / XP
    Mac OS X | **iMac / Macbook
    Mac OS X | **iMac / Macbook
    Enjoy offline reading with these devices
    Apple Devices
    Android Devices
    Windows Devices
    Mac Devices
    iPad, iPhone, iPod
    Our reader is compatible
     
     
     
    Android 2.2 +
     
    Our reader is compatible
     
     
    Kindle Fire
     
    Our reader is compatible
     
     
    Windows
    10 / 8 / 7 / Vista / XP
     
     
    Our reader is compatible
     
    Mac
     
     
     
    Our reader is compatible
List Price: $158.82

Rent Textbook

Select for Price
Add to Cart
There was a problem. Please try again later.

Rent Digital

Rent Digital Options
Online:1825 Days access
Downloadable:Lifetime Access
$70.80
*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.
$70.80*
Add to Cart

New Textbook

We're Sorry
Sold Out

Used Textbook

We're Sorry
Sold Out

Buy from our Marketplace starting at $27.49

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

Summary

Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need.

Following the footsteps of Poincare, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form.

In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced students of nonlinear dynamics interested in learning a rigorous mathemati

Table of Contents

Preface ix
Basic Concepts
1(20)
Necessary background from the theory of ordinary differential equations
1(5)
Dynamical systems Basic notions
6(6)
Qualitative integration of dynamical systems
12(9)
Structurally Stable Equilibrium States Of Dynamical Systems
21(90)
Notion of an equilibrium state. A linearized system
21(3)
Qualitative investigation of 2- and 3-dimensional linear systems
24(13)
High-dimensional linear systems. Invariant subspaces
37(10)
Behavior of trajectories of a linear system near saddle equilibrium states
47(9)
Topological classification of structurally stable equilibrium states
56(9)
Stable equilibrium states. Leading and non-leading manifolds
65(13)
Saddle equilibrium states. Invariant manifolds
78(7)
Solution near a saddle. The boundary-value problem
85(10)
Problem of smooth linearization Resonances
95(16)
Structurally Stable Periodic Trajectories of Dynamical Systems
111(124)
A Poincare map. A fixed point. Multipliers
112(3)
Non-degenerate linear one- and two-dimensional maps
115(10)
Fixed points of high-dimensional linear maps
125(3)
Topological classification of fixed points
128(7)
Properties of nonlinear maps near a stable fixed point
135(6)
Saddle fixed points. Invariant manifolds
141(13)
The boundary-value problem near a saddle fixed point
154(14)
Behavior of linear maps near saddle fixed points. Examples
168(13)
Geometrical properties of nonlinear saddle maps
181(5)
Normal coordinates in a neighborhood of a periodic trajectory
186(8)
The variational equations
194(7)
Stability of periodic trajectories. Saddle periodic trajectories
201(8)
Smooth equivalence and resonances
209(9)
Autonomous normal forms
218(5)
The principle of contraction mappings. Saddle maps
223(12)
Invariant Tori
235(34)
Non-autonomous systems
236(6)
Theorem on the existence of an invariant torus. The annulus principle
242(16)
Theorem on persistence of an invariant torus
258(6)
Basics of the theory of circle diffeomorphisms. Synchronization problems
264(5)
Center Manifold. Local Case
269(56)
Reduction to the center manifold
273(13)
A boundary-value problem
286(16)
Theorem on invariant foliation
302(12)
Proof of theorems on center manifolds
314(11)
Center Manifold. Non-Local Case
325(32)
Center manifold theorem for a homoclinic loop
326(8)
The Poincare map near a homoclinic loop
334(11)
Proof of the center manifold theorem near a homoclinic loop
345(3)
Center manifold theorem for heteroclinic cycles
348(9)
Appendix A. Special Form of Systems Near a Saddle Equilibrium State 357(14)
Appendix B. First Order Asymptotic for the Trajectories Near a Saddle Fixed Point 371(10)
Bibliography 381(8)
Index 389

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.