@article{He2025, 
author = {Shengnan He and Zongbin Yin},
title = {Frequently hypercyclic and Devaney chaotic        C          0      -semigroups indexed by complex sectors},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {20505-20530},
keywords = {frequent hypercyclicity, Devaney chaos, complex sector, C0-semigroups, translation semigroup, periodic point},
url = {https://www.sciopen.com/article/10.3934/math.2025915},
doi = {10.3934/math.2025915},
abstract = {In this paper, the definitions of frequent hypercyclicity and Devaney chaos for a        C    0  -semigroup              {              T                  t                    }              t      ∈      Δ       indexed by a complex sector    Δ are revisited. A general sufficient criterion and necessary conditions for a        C    0  -semigroup              {              T                  t                    }              t      ∈      Δ       to be frequently hypercyclic are established. By adapting the concept of periodic point with a syndetic set of periods, we present clean and effective characterizations of the Devaney chaotic translation semigroup              {              T                  t                    }              t      ∈      Δ       on        L          ρ              p        (  Δ  ,      K    )  ,  1  ≤  p  <  ∞, which generalize those of the classical translation semigroup              {              T                  t                    }              t      ≥      0      . Moreover, it is shown that Devaney chaos implies frequent hypercyclicity, topological mixing, and distributional chaos for the translation semigroups              {              T                  t                    }              t      ∈      Δ       under our revised definitions, and that topological mixing or distributional chaos does not imply Devaney chaos.}
}