A refinement of Sharkovskii's theorem on orbit types characterized by two parameters

TL;DR

This paper refines Sharkovskii's theorem by addressing the type problem, focusing on specific orbit types characterized by two parameters to deepen the understanding of orbit forcing in dynamical systems.

Contribution

It provides a new solution to the type problem, offering a refined version of Sharkovskii's theorem for orbit types with two parameters.

Findings

Solution to the type problem for specific orbit types

Refinement of Sharkovskii's theorem based on two-parameter orbit types

Enhanced understanding of orbit forcing in dynamical systems

Abstract

The so-called type problem or forcing problem is considered as a way to generalize Sharkovskii's theorem. In this paper, by focusing on certain types of orbits, we obtain a solution of the type problem, which gives a refinement of Sharkovskii's theorem on orbit types characterized by two parameters.