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Sharkovskii Type of Cycles
Author(s) -
Blokh Alexander M.,
Coven Ethan M.
Publication year - 1996
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/28.4.417
Subject(s) - mathematics , integer (computer science) , permutation (music) , type (biology) , combinatorics , interval (graph theory) , set (abstract data type) , point (geometry) , discrete mathematics , geometry , computer science , ecology , physics , acoustics , biology , programming language
The Sharkovskii type of a map of an interval is the Sharkovskii‐greatest integer t such that it has a periodic point of period t . The Sharkovskii type of a cycle (that is, a cyclic permutation) is the Sharkovskii type of the 'connect the dots' map determined by it. For n ⩾ 2, let c ( n ) denote the finite set of integers which are Sharkovskil types of n ‐cycles. We give an internal characterization of c ( n ) and an n 4 ‐time algorithm for determining the Sharkovskii type of an n ‐cycle.