Some relations between Bohl exponents and the exponential dichotomy spectrum

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 a spectral interval.

KEYWORDS:

• Bohl exponents
• exponential dichotomy spectrum
• difference equations

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 39A06
• 39A12
• 39A22

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research has been partially supported by FONDECYT Regular 1170968.