TY - JOUR

T1 - Ergodicity in nonautonomous linear ordinary differential equations

AU - Pituk, M.

AU - Pötzsche, Christian

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The weak and strong ergodic properties of nonautonomous linear ordinary differential equations are considered. It is shown that if the coefficient matrix function is bounded, essentially nonnegative and uniformly irreducible, then the normalized positive solutions are asymptotically equivalent to the Perron vectors of the strongly positive transition matrix at infinity (weak ergodicity). If, in addition, the coefficient matrix function is uniformly continuous, then the convergence of the normalized positive solutions to the same strongly positive limiting vector (strong ergodicity) is equivalent to the convergence of the Perron vectors of the coefficient matrices.

AB - The weak and strong ergodic properties of nonautonomous linear ordinary differential equations are considered. It is shown that if the coefficient matrix function is bounded, essentially nonnegative and uniformly irreducible, then the normalized positive solutions are asymptotically equivalent to the Perron vectors of the strongly positive transition matrix at infinity (weak ergodicity). If, in addition, the coefficient matrix function is uniformly continuous, then the convergence of the normalized positive solutions to the same strongly positive limiting vector (strong ergodicity) is equivalent to the convergence of the Perron vectors of the coefficient matrices.

KW - Ergodicity

KW - Hilbert's projective metric

KW - Ordinary differential equation

KW - Perron–Frobenius theory

KW - Positivity

UR - http://www.scopus.com/inward/record.url?scp=85068466503&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068466503&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2019.07.005

DO - 10.1016/j.jmaa.2019.07.005

M3 - Article

AN - SCOPUS:85068466503

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

ER -