# Disjoint distributional chaos in Fr\'echet spaces

## TL;DR

This paper introduces new concepts of disjoint distributional chaos for sequences of multivalued linear operators in Fréchet spaces, expanding the understanding of chaotic behavior in advanced functional analysis.

## Contribution

It presents novel notions of disjoint distributional chaos, not previously studied even for linear operators in Banach spaces, along with analysis and examples of such behavior.

## Key findings

- New notions of disjoint distributional chaos introduced
- Identification of specific classes of operators exhibiting chaotic behavior
- Provision of numerous examples and applications

## Abstract

We introduce several different notions of disjoint distributional chaos for sequences of multivalued linear operators in Fr\'echet spaces. Any of these notions seems to be new and not considered elsewhere even for linear continuous operators in Banach spaces. We focus special attention to the analysis of some specific classes of linear continuous operators having a certain disjoint distributionally chaotic behaviour, providing also a great number of illustrative examples and applications of our abstract theoretical results.