The hypocoercivity index for the short time behavior of linear time-invariant ODE systems
Dynamical Systems
2026-01-30 v5
Abstract
We consider the class of conservative-dissipative ODE systems, which is a subclass of Lyapunov stable, linear time-invariant ODE systems. We characterize asymptotically stable, conservative-dissipative ODE systems via the hypocoercivity (theory) of their system matrices. Our main result is a concise characterization of the hypocoercivity index (an algebraic structural property of matrices with positive semi-definite Hermitian part introduced in Achleitner, Arnold, and Carlen (2018)) in terms of the short time behavior of the propagator norm for the associated conservative-dissipative ODE system.
Keywords
Cite
@article{arxiv.2109.10784,
title = {The hypocoercivity index for the short time behavior of linear time-invariant ODE systems},
author = {Franz Achleitner and Anton Arnold and Eric A. Carlen},
journal= {arXiv preprint arXiv:2109.10784},
year = {2026}
}