Sharkovskii Type of Cycles
- Resource Type
- Authors
- Ethan M. Coven; Alexander Blokh
- Source
- Bulletin of the London Mathematical Society. 28:417-424
- Subject
- Combinatorics
Integer
General Mathematics
Periodic point
Interval (graph theory)
Characterization (mathematics)
Type (model theory)
Finite set
Mathematics
Cyclic permutation
- Language
- ISSN
- 0024-6093
The Sharkovskĭi type of a map of an interval is the Sharkovskĭi-greatest integer t such that it has a periodic point of period t. The Sharkovskĭi type of a cycle (i.e., a cyclic permutation) is the Sharkovskĭi type of the “connect the dots” map determined by it. For n ≥ 2, let C(n) denote the finite set of integers which are Sharkovskĭi types of n-cycles. We give an internal characterization of C(n) and an n4-time algorithm for determining the Sharkovskĭi type of an n-cycle.