Dynamics and Bifurcations

by Hale, Jack K.; Kocak, Huseyin

• ISBN13: 9780387971414
• ISBN10: 0387971416
• Format: Hardcover
• Copyright: 1991-12-01
• Publisher: Springer Nature

Summary

The subject of differential and difference equations is an old and much-honored chapter in science, one which germinated in applied fields such as celestial mechanics, nonlinear oscillations, and fluid dynamics. In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications with perhaps a more mature look. Many of the available books and expository narratives either require extensive mathematical preparation, or are not designed to be used as textbooks. The authors have filled this void with the present book.

Table of Contents

PART I: Dimension One
Scalar Autonomous Equations
Existence and Uniqueness	4	(4)
Geometry of Flows	8	(8)
Stability of Equilibria	16	(5)
Equations on a Circle	21	(5)
Elementary Bifurcations
Dependence on Parameters--Examples	26	(15)
The Implicit Function Theorem	41	(1)
Local Perturbations Near Equilibria	42	(12)
An Example on a Circle	54	(2)
Computing Bifurcation Diagrams	56	(5)
Equivalence of Flows	61	(7)
Scalar Maps
Euler's Algorithm and Maps	68	(4)
Geometry of Scalar Maps	72	(9)
Bifurcations of Monotone Maps	81	(6)
Period-doubling Bifurcation	87	(5)
An Example: The Logistic Map	92