UDC

515.16

Authors

Starostina Vera Valeryevna, Postgraduate Student, Institute of Mathematics, Information and Space Technologies, Northern (Arctic) Federal University named after M.V. Lomonosov (Arkhangelsk, Russia)

Teplyakov Vyacheslav Vasilyevich, Institute of Mathematics, Information and Space Technologies, Northern (Arctic) Federal University named after M.V. Lomonosov (Arkhangelsk, Russia)

Abstract

The paper demonstrates the way of constructing examples showing that for any natural p there exists a continuous map f: I → I that has a period p and does not have any periods preceding p in Sharkovsky sequence.

Keywords

orbit, period, cycle, Sharkovsky sequence, period doubling.

References

1. Katok A.B., Khasselblat B. Vvedenie v sovremennuyu teoriyu dinamicheskikh sistem [Introduction to the Modern Dynamical Systems Theory]. Moscow, 1999.
2. Sharkovskiy A.N. Sosushchestvovanie tsiklov nepreryvnogo otobrazheniya pryamoy v sebya [Coexistence of Cycles of Continuous Mapping of a Line to Itself]. Ukrainskiy matematicheskiy zhurnal, 1964, vol. 16, no. 1.