Linear dynamics of semigroups generated by differential operators

J. Alberto Conejero, et al. "Linear dynamics of semigroups generated by differential operators." Open Mathematics 15.1 (2017): 745-767. <http://eudml.org/doc/288323>.

@article{J2017,
abstract = {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.},
author = {J. Alberto Conejero, Carlos Lizama, Marina Murillo-Arcila, Alfredo Peris},
journal = {Open Mathematics},
keywords = {Hypercyclicity; Topological transitivity; Topologically mixing property; Devaney chaos; C0-semigroups},
language = {eng},
number = {1},
pages = {745-767},
title = {Linear dynamics of semigroups generated by differential operators},
url = {http://eudml.org/doc/288323},
volume = {15},
year = {2017},
}

TY - JOUR
AU - J. Alberto Conejero
AU - Carlos Lizama
AU - Marina Murillo-Arcila
AU - Alfredo Peris
TI - Linear dynamics of semigroups generated by differential operators
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 745
EP - 767
AB - 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.
LA - eng
KW - Hypercyclicity; Topological transitivity; Topologically mixing property; Devaney chaos; C0-semigroups
UR - http://eudml.org/doc/288323
ER -