On common periodic points conjecture, history and some related questions
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CitationAlikhani-Koopaei, A. (2009). On common periodic points conjecture, history and some related questions. Maltepe Üniversitesi. s. 88.
From 1954 to 1969 there was a rather well known conjecture, namely the common fixed point conjecture, that if f and g are continuous functions from the closed unit interval to itself which commute, meaning f(g(x)) = g(f(x)), then they have a common fixed point. In  and , W.M. Boyce and J.P. Huneke answered this question independently by the construction of a pair of commuting continuous functions which have no fixed point in common. This conjecture led us to introduce the common periodic point conjecture (see ) which reads as: Conjecture. If f and g are continuous functions from [0, 1] to itself which commute (i.e. f(g(x)) = g(f(x))), then they must have a common periodic point. In fact we conjectured that typically commuting continuous self-maps of closed intervals do not share a periodic point. In this talk we give the history of this conjecture as well as some related results and some open questions.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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