During the last years, several notions have been introduced for describing the dynamical behavior of linear operators on infinite-dimensional spaces, such as hypercyclicity, chaos in the sense of Devaney, chaos in the sense of Li-Yorke, subchaos, mixing and weakly mixing properties, and frequent hypercyclicity, among others. These notions have been extended, as far as possible, to the setting of C0-semigroups of linear and continuous operators. We will review some of these notions and we will discuss basic properties of the dynamics of C0-semigroups. We will also study in detail the dynamics of the translation C0-semigroup on weighted spaces of integrable functions and of continuous functions vanishing at infinity. Using the comparison lemma, these results can be transferred to the solution C0-semigroups of some partial differential equations. Additionally, we will also visit the chaos for infinite systems of ordinary differential equations, that can be of interest for representing birth-and-death process or car-following traffic models.
@article{bwmeta1.element.doi-10_1515_math-2017-0065,
author = {J. Alberto Conejero and Carlos Lizama and Marina Murillo-Arcila and Alfredo Peris},
title = {Linear dynamics of semigroups generated by differential operators},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {745-767},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0065}
}
J. Alberto Conejero; Carlos Lizama; Marina Murillo-Arcila; Alfredo Peris. Linear dynamics of semigroups generated by differential operators. Open Mathematics, Tome 15 (2017) pp. 745-767. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0065/