Coexistence of cycles of а continuous mapping of the line into itself

• Date: 2024
• Main Authors: Sharkovsky, O. M., Шарковський, О. М.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2024
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8026
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.9 Our main result can be formulated as follows:   Consider the set of natural numbers in which the following relation is introduced: $n_1$ precedes $n_2$ $(n_1 \preceq n_2)$ if, for any continuous mappings of the real line into itself, the existence of а cycle...