The Sharkovsky program of classification of triangular maps -- a survey (Q2800392)

There are more than 50 mutually equivalent conditions for a continuous interval map to have zero topological entropy. Many of these conditions transfer to the context of triangular maps of the square (the canonical list of them is 32 items long). The Sharkovsky program of classification of triangular maps called for an investigation of the possible implications between them; it was launched in the 1980's and finally completed in 2013.NEWLINENEWLINEThis article is a thorough survey of the work that has been done on it by multiple authors and includes the detailed list of the 32 conditions, an overview of important and related concepts, and a full summary of the results.