Periodic sequences and chaos for a bimodal map

A type of mapping from [0, 1] to [0, 1] which has two maximal points has be en considered, and its periodic points and chaotic behavior have been discu ssed. Two types of periodic point sequences have been found: one is the Sar kovskii's order and the other is the inverse natural number order. The univ ersal numbers for these two periodic point sequences are also given by nume rical methods. A new universal number which is very different from the Feig enbaum's number is obtained.