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Book Review
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Book Information
Editor(s):
Brian R. Hunt, Judy A. Kennedy, Tien-Yien Li and Helena E. Nusse.
Title:
The theory of chaotic attractors
Additional book information:
Springer-Verlag,
New York,
2004,
vi+514,
US$69.95,
0-387-40349-3
References:
-
- 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 (93k:58140)
- 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 (98a:58113)
- 3.
- M. Benedicks and L. Carleson, The dynamics of the Hénon map, Annals of Math. 133 (1991), 73-169. MR 1087346 (92d:58116)
- 4.
- J. Gleick, Chaos: Making a New Science, Viking Penguin, Inc., New York, 1987. MR 1010647 (91d:58152)
- 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 (85d:58062)
- 6.
- M. Jakobson, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Commun. Math. Phys. 81 (1981), 39-88. MR 0630331 (83j:58070)
- 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 (94c:58135)
- 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 (80k:58074)
- 9.
- D. Ruelle and F. Takens, On the nature of turbulence, Commun. Math. Phys. 20 (1971), 167-192. MR 0284067 (44:1297)
- 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 (28:3121)
- 11.
- Ya.G. Sinai, Gibbs measures in ergodic theory, Russian Mathematical Surveys 27 (1972), 21-69. MR 0399421 (53:3265)
- 12.
- S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 0228014 (37:3598)
- 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 (85b:58089)
Additional Information:
Reviewer(s):
Kathleen
T.
Alligood
Affiliation:
George Mason University
Email:
alligood@gmu.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
44
(2007),
317-321.
MSC
(2000):
Primary 37D45, 37A40, 37C40, 37Exx, 28D05, 01A75
DOI:
10.1090/S0273-0979-06-01134-7
PII:
S 0273-0979(06)01134-7
Posted:
November 7, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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