Abstract
Numerical studies of a map that models the rotation of a periodically kicked rotor with friction reveal chaotic attractors. At parameter values that precede the existence of a horseshoe a chaotic attractor is found. The growth and destruction of this attractor are studied in relation to the early stages of the formation of a horseshoe in the region. A pattern, also seen in a Hénon map, is that of a “crisis” which occurs as the parameter increases2. The chaotic attractor has 2n pieces upon collision with an orbit of period 3×2n. This crisis marks the destruction of the attractor. The value of n depends on the Jacobian of the map.
This research was partially supported by the Air Force Office of Scientific Research under grant AF0SR-81-0217 and by the National Science Foundation under grant MCS 81-17967.
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References
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© 1984 Springer-Verlag Berlin Heidelberg
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Short, T., Yorke, J.A. (1984). Truncated Development of Chaotic Attractors in a Map when the Jacobian is not Small. In: Kuramoto, Y. (eds) Chaos and Statistical Methods. Springer Series in Synergetics, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69559-9_3
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DOI: https://doi.org/10.1007/978-3-642-69559-9_3
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