# Some relations between Bohl Exponents and the Exponential Dichotomy spectrum

## TL;DR

This paper explores the relationship between Bohl's exponents and the exponential dichotomy spectrum in non-autonomous linear difference systems, establishing that Bohl's exponents lie within spectral intervals for initial conditions in invariant bundles.

## Contribution

It demonstrates a connection between Bohl's exponents and the exponential dichotomy spectrum, providing bounds for exponents within spectral intervals in difference equations.

## Key findings

- Bohl's exponents are contained in spectral intervals.
- The relationship holds for initial conditions in invariant bundles.
- Provides a spectral characterization of Bohl's exponents.

## Abstract

We study a liaison between the Bohl's exponents and the exponential dichotomy spectrum of a non autonomous linear system of difference equations on the whole line $\mathbb{Z}$. More specifically, We prove that for any initial condition in an invariant vector bundle, associated to its exponential dichotomy spectrum, its Bohl's exponents are contained in an spectral interval.