COEXISTENCE OF CYCLES OF A CONTINUOUS MAP OF THE LINE INTO ITSELF

✍ Scribed by SHARKOVSKIĬ, A. N.

• Book ID: 121016932
• Publisher: World Scientific Publishing Company
• Year: 1995
• Tongue: English
• Weight: 567 KB
• Volume: 05
• Category: Article
• ISSN: 0218-1274
• DOI: 10.1142/S0218127495000934

✦ Synopsis

The basic result of this investigation may be formulated as follows. Consider the set of natural numbers in which the following relationship is introduced: n~1~ precedes n~2~ (n~1~ ≼ n~2~) if for any continuous mapping of the real line into itself the existence of a cycle of order n~2~ follows from the existence of a cycle of order n~1~. The following theorem holds.