On common periodic points conjecture, history and some related questions
Küçük Resim Yok
Tarih
2009
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
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 [2] and [3], 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 [1]) 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.
Açıklama
Anahtar Kelimeler
Kaynak
International Conference of Mathematical Sciences
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Alikhani-Koopaei, A. (2009). On common periodic points conjecture, history and some related questions. Maltepe Üniversitesi. s. 88.
