Abstract

For continuous interval maps we formulate a conjecture on the shape of the cycles of maximum topological entropy of period 4k+2. We also present numerical support for the conjecture. This numerical support is of two different kinds. For periods 6, 10, 14 and 18 we are able to compute the maximum entropy cycles by using non-trivial, ad hoc numerical procedures and the known results of Jungreis (1991). In fact, the conjecture we formulate is based on these results.
For periods n=22, 26 and 30 we compute the maximum entropy cycle of a restricted subfamily of cycles. The obtained results agree with the conjectured ones. The conjecture that we can restrict our attention to this subfamily is motivated theoretically.