A note on discrete monotonic dynamical systems

TL;DR

This paper establishes an upper bound on the Lebesgue measure of points in a discrete monotonic dynamical system where the system exhibits robustness, under specific conditions on the function and domain.

Contribution

It provides a new upper bound for the measure of robust points in discrete monotonic systems with certain conditions on the function and domain.

Findings

Derived an explicit upper bound for Lebesgue measure of robust points

Applicable to systems with monotonic functions satisfying specific conditions

Enhances understanding of robustness in discrete dynamical systems

Abstract

We give a upper bound of Lebesgue measure $V(S(f,h,\Omega))$ of the set $S(f,h,\Omega)$ of points $q\in Q_h^d$ for which the triple $(h,q,\Omega)$ is dynamically robust when $f$ is monotonic and satisfies certain condition on some compact subset $\Omega \in \mathbb{R}^d$.