An abstract version of Lyapunov exponents is defined for positive homogeneous maps on Homogeneous Lattices and a sufficient condition is given for the asymptotic stability of the map.
EDEN, ALP (2000) "A Remark on the Asymptotic Properties of Positive Homogeneous Maps on Homogeneous Lattices," Turkish Journal of Mathematics: Vol. 24: No. 3, Article 8. Available at: https://journals.tubitak.gov.tr/math/vol24/iss3/8