Search for cycles in non-linear autonomous discrete dynamical system

TL;DR

This paper introduces a new polynomial family and a robust algorithm for detecting cycles of any length in non-linear autonomous discrete dynamical systems, supported by numerical examples.

Contribution

It presents a novel polynomial family and an algorithm for cycle detection in non-linear discrete systems, extending previous methods.

Findings

The polynomial family includes Fejér and Suffridge polynomials as special cases.

The proposed algorithm effectively detects cycles of arbitrary length.

Numerical examples demonstrate the algorithm's practical applicability.

Abstract

We construct a family of polynomials with real coefficients that contains as a particular case the Fej\'er and Suffridge polynomials. These polynomials allow us to suggest a robust algorithm to search for cycles of arbitrary length in non-linear autonomous discrete dynamical systems. Numeric examples are included.