Sharkovskii's ordering and estimates of the number of periodic trajectories of given period of a self-map of an interval

DOI10.1134/S1063454119030099zbMath1427.37030OpenAlexW2974192885MaRDI QIDQ2282759

O. A. Ivanov

Publication date: 19 December 2019

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1063454119030099

zbMATH Keywords

periodic trajectorySharkovskii ordermap of intervalpath in directed graph

Mathematics Subject Classification ID

Dynamical systems involving maps of the interval (37E05) Combinatorial dynamics (types of periodic orbits) (37E15) Dynamical systems involving maps of trees and graphs (37E25)

Cites Work

• A theorem of Sarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line
• An estimate for the number of periodical trajectories of the given period for mapping of an interval, Lucas numbers, and necklaces
• The minimal number of periodic orbits of periods guaranteed in Sharkovskii's theorem
• Period Three Implies Chaos
• COEXISTENCE OF CYCLES OF A CONTINUOUS MAP OF THE LINE INTO ITSELF
• On a Converse of Sharkovsky's Theorem
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