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Dynamics and Bifurcations : Texts in Applied Mathematics - Huseyin Kocak

Dynamics and Bifurcations

Texts in Applied Mathematics

Hardcover Published: 15th November 1996
ISBN: 9780387971414
Number Of Pages: 574

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In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.

J.K. Hale, H. Kocak, and H. Buttanri

Dynamics and Bifurcations

"This book takes the reader step by step through the vast subject of dynamical systems. Proceeding from 1 to 2 dimensions and onto higher dimensions in separate self-contained sections, the text is mathematically rigorous yet devoid of excess formalism. A refreshing balance is further achieved by the use of many excellent illustrations and a wealth of worked and unworked examples."-MATHEMATIKA

Dimension One
Scalar Autonomous Equations
Elementary Bifurcations
Scalar Maps
Dimension One and One Half
Scalar Nonautonomous Equations
Bifurcation of Periodic Equations
On Tori and Circles
Dimension Two
Planar Autonomous Systems
Linear Systems
Near Equilibria
In the Presence of a Zero Eigenvalue
In the Presence of Purely Imaginary Eigenvalues
Periodic Orbits
All Planar Things Considered
Conservative and Gradient Systems
Planar Maps
Higher Dimensions
Dimension Two and One Half
Dimension Three
Dimension Four
Farewell
A Catalogue of Fundamental Theorems
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387971414
ISBN-10: 0387971416
Series: Texts in Applied Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 574
Published: 15th November 1996
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.4 x 15.6  x 3.18
Weight (kg): 1.01
Edition Number: 3