Abstract
This paper shows that if a horseshoe is created in a natural manner as a parameter is varied, then the process of creation involves the appearance of attracting periodic orbits of all periods. Furthermore, each of these orbits will period double repeatedly, with those periods going to infinity.
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Communicated by O. E. Lanford
In memory of Charles Conley
Research partially supported by the National Science Foundation
Research partially supported by the Air Force Office of Scientific Research
The paper was written while Dr. Alligood was visiting Michigan State University and the University of Maryland
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Yorke, J.A., Alligood, K.T. Period doubling cascades of attractors: A prerequisite for horseshoes. Commun.Math. Phys. 101, 305–321 (1985). https://doi.org/10.1007/BF01216092
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DOI: https://doi.org/10.1007/BF01216092