# Rendezvous with Sensitivity

## TL;DR

This paper surveys various types of sensitivity in compact dynamical systems, exploring their properties and implications, highlighting the role of sensitivity as a fundamental aspect of unpredictability.

## Contribution

It provides a comprehensive overview of different sensitivity notions in dynamical systems and their interrelations, emphasizing their significance in understanding system unpredictability.

## Key findings

- Sensitivity implies unpredictability in dynamical systems.
- Different sensitivity notions are interconnected and have specific properties.
- Sensitivity properties can be used to characterize complex dynamical behaviors.

## Abstract

Let $(X,d)$ be a compact metric space and $f:X \to X$ be a self-map. The compact dynamical system $(X,f)$ is called sensitive or sensitivity depends on initial conditions, if there is a positive constant $\delta$ such that in each non-empty open subset there are distinct points whose iterates will be $\delta-$apart at same instance. This dynamical property, though being a very weak one, brings in the essence of unpredictability in the system. In this article, we survey various sensitivities and some properties implied by and implying such sensitivities.