Computational Complexity of Iterated Maps on the Interval (Extended Abstract)

TL;DR

This paper analyzes the computational complexity of calculating orbits in discrete dynamical systems on the interval, linking it to the Lyapunov exponent, and presents a verified algorithm based on error analysis.

Contribution

It introduces a general algorithm for exact orbit computation with proven correctness and relates its complexity to the Lyapunov exponent of the system.

Findings

Complexity measure is related to the Lyapunov exponent.

A multiple-precision floating point algorithm is proposed.

The algorithm's correctness is formally proven.

Abstract

The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the computational complexity is analyzed. As a main result, the computational complexity measure considered here is related to the Ljapunow exponent of the dynamical system under consideration.