The Number of Periods in One-Dimensional Gap Map and Lorenz-Like Map |
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Authors: | Fa-Gen XIE Bai-Lin HA |
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Affiliation: | 1. Department of Physics, Beijing Normal University, Beijing 100875, China;2. Institute of Theoretical Physics, Academia Sinica, Beijing 100080, China |
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Abstract: | The problem of coun ting the number of periods in one-dimensional maps is extended to two discontinuous maps, the gap map and the Lorenz-like map. The numbers of periods in the gap map and the Lorenz-like map are given by 4F2(n) and 2C2(n), respectively, where F2(n) and C2 (n) are the number of periodic sequences, invariant under group Cn S2 and Cn, respectively. |
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