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Bulletin of the American Mathematical Society

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Cascades of period-doubling bifurcations: A prerequisite for horseshoes


Authors: James A. Yorke and Kathleen T. Alligood
Journal: Bull. Amer. Math. Soc. 9 (1983), 319-322
MSC (1980): Primary 58F12, 58F13, 58F14, 58F20
DOI: https://doi.org/10.1090/S0273-0979-1983-15191-1
MathSciNet review: 714994
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References [Enhancements On Off] (What's this?)

  • 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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DOI: https://doi.org/10.1090/S0273-0979-1983-15191-1

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