The Theory of Chaotic Attractors

by Hunt, Brian R.; Kennedy, Judy A.; Li, Tien-Yien; Nusse, Helena Engelina; Kennedy, Judy A.

• ISBN13: 9780387403496
• ISBN10: 0387403493
• Format: Hardcover
• Copyright: 2004-01-01
• Publisher: Springer Nature

Summary

This volume contains a selection of the most important papers in the theory of chaotic attractors over the past 40 years. It is dedicated to James Yorke - a pioneer in the field and a recipient of the 2003 Japan prize - on the occasion of his 60th birthday. The volume includes an introduction to Yorke's work and an overview of key developments in the theory of chaotic attractors.

Table of Contents

Preface	vii
Introduction	1	(24)
Deterministic Nonperiodic Flow	25	(12)
E.N. Lorenz
On Invariant Measures for Expanding Differentiable Mappings	37	(10)
K. Krzyzewski
W. Szlenk
On the Existence of Invariant Measures for Piecewise Monotonic Transformations	47	(8)
A. Lasota
J.A. Yorke
The Ergodic Theory of Axiom A Flows	55	(22)
R. Bowen
D. Ruelle
Period Three Implies Chaos	77	(8)
T.-Y. Li
J.A. Yorke
Simple Mathematical Models with Very Complicated Dynamics	85	(9)
R.M. May
A Two-Dimensional Mapping with a Strange Attractor	94	(9)
M. Henon
Strange Attractors and Chaotic Motions of Dynamical Systems	103	(17)
E. Ott
Ergodic Properties of Invariant Measures for Piecewise Monotonic Transformations	120	(22)
F. Hofbauer
G. Keller
The Dimension of Chaotic Attractors	142	(28)
D. J. Farmer
E. Ott
J.A. Yorke
Measuring the Strangeness of Strange Attractors	170	(20)
P. Grassberger
I. Procaccia
Invariant Measures and Variational Principle for Lozi Applications	190	(32)
M. Rychlik
Ergodic Properties of The Lozi Mappings	222	(21)
P. Collet
Y. Levy
On the Concept of Attractor	243	(22)
J. Milnor
Bowen-Ruelle Measures for Certain Piecewise Hyperbolic Maps	265	(8)
L.-S. Young
Ergodic Theory of Chaos and Strange Attractors	273	(40)
J.-P. Eckmann
D. Ruelle
Another Proof of Jakobson's Theorem and Related Results	313	(22)
M.R. Rychlik
Unstable Periodic Orbits and the Dimensions of Multifractal Chaotic Attractors	335	(14)
C. Grebogi
E. Ott
J.A. Yorke
Absolutely Continuous Invariant Measures for Piecewise Expanding C2 Transformation in RN	349	(15)
P. Gora
A. Boyarsky
Sinai-Bowen-Ruelle Measures for Certain Henon Maps	364	(36)
M. Benedicks
L.-S. Young
On the Approximation of Complicated Dynamical Behavior	400	(25)
M. Dellnitz
O. Junge
Absolutely Continuous Invariant Measures for Piecewise Real-Analytic Expanding Maps on the Plane	425	(18)
M. Tsujii
SRB Measures for Partially Hyperbolic Systems Whose Central Direction is Mostly Expanding	443	(48)
J.F. Alves
C. Bonatti
M. Viana
SLYRB Measures: Natural Invariant Measures for Chaotic Systems	491	(22)
B.R. Hunt
J.A. Kennedy
T.-Y. Li
H.E. Nusse
Credits	513