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Cascades of period-doubling bifurcations: A prerequisite for horseshoes
Author(s):
James A.
Yorke;
Kathleen T.
Alligood
Journal:
Bull. Amer. Math. Soc.
9
(1983),
319-322.
MSC (1980):
Primary 58F12, 58F13, 58F14, 58F20
MathSciNet review:
714994
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References |
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Additional information
References:
- 1.
- K. T. Alligood, J. Mallet-Paret and J. A. Yorke, An index for the global continuation of relatively isolated sets of periodic orbits, Proc. Dynamics Sympos. IMPA, Rio de Janeiro, 1981 (to appear). MR 730259
- 2.
- K. T. Alligood and J. A. Yorke, Families of periodic orbits: virtual periods and global continuability, J. Differential Equations (to appear). MR 759827
- 3.
- S. N. Chow, J. Mallet-Paret and J. Yorke, A bifurcation invariant: degenerate orbits treated as clusters of simple orbits, Proc. Dynamics Sympos. IMPA, Rio de Janeiro, 1981 (to appear).
- 4.
- J. Mallet-Paret and J. Yorke, Snakes: oriented families of periodic orbits, their sources, sinks and continuation, J. Differential Equations 43 (1982), 419-450. MR 649847
- 5.
- S. Newhouse, Lectures on dynamical systems, Dynamical Systems, Progress in Mathematics, Vol. 8, Birkhäuser, Boston, 1980. MR 589590
- 6.
- C. Robinson, Bifurcation to infinitely many sinks, preprint. MR 719300
- 7.
- S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 228014
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58F12, 58F13, 58F14, 58F20
Additional Information:
DOI:
10.1090/S0273-0979-1983-15191-1
PII:
S 0273-0979(1983)15191-1
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