Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Full text of review:
PDF
This review is available free of charge.
Book Information:
Editors:
Brian R. Hunt,
Judy A. Kennedy,
Tien-Yien Li and
Helena E. Nusse
Title:
The theory of chaotic attractors
Additional book information:
edited by
Brian R. Hunt,
Judy A. Kennedy,
Tien-Yien Li and
Helena E. Nusse,
Springer-Verlag,
New York,
2004,
vi+514 pp.,
ISBN 0-387-40349-3,
US$69.95$
J. C. Alexander, James A. Yorke, Zhiping You, and I. Kan, Riddled basins, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 2 (1992), no. 4, 795–813. MR 1206103, DOI 10.1142/S0218127492000446
Kathleen T. Alligood, Tim D. Sauer, and James A. Yorke, Chaos, Textbooks in Mathematical Sciences, Springer-Verlag, New York, 1997. An introduction to dynamical systems. MR 1418166, DOI 10.1007/978-3-642-59281-2
Michael Benedicks and Lennart Carleson, The dynamics of the Hénon map, Ann. of Math. (2) 133 (1991), no. 1, 73–169. MR 1087346, DOI 10.2307/2944326
James Gleick, Chaos, Penguin Books, New York, 1987. Making a new science. MR 1010647
Celso Grebogi, Edward Ott, and James A. Yorke, Crises, sudden changes in chaotic attractors, and transient chaos, Phys. D 7 (1983), no. 1-3, 181–200. Order in chaos (Los Alamos, N.M., 1982). MR 719052, DOI 10.1016/0167-2789(83)90126-4
M. V. Jakobson, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981), no. 1, 39–88. MR 630331
Ittai Kan, Hüseyin Koçak, and James A. Yorke, Antimonotonicity: concurrent creation and annihilation of periodic orbits, Ann. of Math. (2) 136 (1992), no. 2, 219–252. MR 1185119, DOI 10.2307/2946605
James L. Kaplan and James A. Yorke, Chaotic behavior of multidimensional difference equations, Functional differential equations and approximation of fixed points (Proc. Summer School and Conf., Univ. Bonn, Bonn, 1978) Lecture Notes in Math., vol. 730, Springer, Berlin, 1979, pp. 204–227. MR 547989
David Ruelle and Floris Takens, On the nature of turbulence, Comm. Math. Phys. 20 (1971), 167–192. MR 284067
O. M. Šarkovs′kiĭ, Co-existence of cycles of a continuous mapping of the line into itself, Ukrain. Mat. . 16 (1964), 61–71 (Russian, with English summary). MR 0159905
Ja. G. Sinaĭ, Gibbs measures in ergodic theory, Uspehi Mat. Nauk 27 (1972), no. 4(166), 21–64 (Russian). MR 0399421
S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1
James A. Yorke and Kathleen T. Alligood, Cascades of period-doubling bifurcations: a prerequisite for horseshoes, Bull. Amer. Math. Soc. (N.S.) 9 (1983), no. 3, 319–322. MR 714994, DOI 10.1090/S0273-0979-1983-15191-1
- 1.
- J.C. Alexander, J.A. Yorke, Z-P. You, and I. Kan, Riddled basins, Int. J. Bifurcation and Chaos 2 (1992), 795-813. MR 1206103
- 2.
- K. Alligood, T. Sauer, and J.A. Yorke, Chaos: An Introduction to Dynamical Systems, Textbooks in Mathematical Sciences, Springer-Verlag, New York, 1997. MR 1418166
- 3.
- M. Benedicks and L. Carleson, The dynamics of the Hénon map, Annals of Math. 133 (1991), 73-169. MR 1087346
- 4.
- J. Gleick, Chaos: Making a New Science, Viking Penguin, Inc., New York, 1987. MR 1010647
- 5.
- C. Grebogi, E. Ott, and J.A. Yorke, Crises, sudden changes in chaotic attractors, and transient chaos, Physica D 7 (1983), 181-200. MR 0719052
- 6.
- M. Jakobson, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Commun. Math. Phys. 81 (1981), 39-88. MR 0630331
- 7.
- I. Kan, H. Kocak, and J.A. Yorke, Antimonotonicity: concurrent creation and annihilation of periodic orbits, Annals of Mathematics 136 (1992), 219-252. MR 1185119
- 8.
- J.L. Kaplan and J.A. Yorke, Chaotic behavior of multidimensional difference equations, in Functional Differential Equations and Approximation of Fixed Points, H.O. Peitgen and H.O. Walther, eds., Springer Lecture Notes in Mathematics #730 (1979), 204-227. MR 0547989
- 9.
- D. Ruelle and F. Takens, On the nature of turbulence, Commun. Math. Phys. 20 (1971), 167-192. MR 0284067
- 10.
- A. N. Sarkovskii, Coexistence of cycles of a continuous mapping of a line into itself, Ukranian Math. Z. 16 (1964), 61-71. MR 0159905
- 11.
- Ya.G. Sinai, Gibbs measures in ergodic theory, Russian Mathematical Surveys 27 (1972), 21-69. MR 0399421
- 12.
- S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 0228014
- 13.
- J.A. Yorke and K. Alligood, Cascades of period-doubling bifurcations: a prerequisite for horseshoes, Bull. Amer. Math. Soc. 9 (1983), 319-322. MR 0714994
Review Information:
Reviewer:
Kathleen T. Alligood
Affiliation:
George Mason University
Email:
alligood@gmu.edu
Journal:
Bull. Amer. Math. Soc.
44 (2007), 317-321
Published electronically:
November 7, 2006
Review copyright:
© Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
