Equicontinuous Actions on Semi-Locally Connected and Local Dendrites

We show a necessary and sufficient condition of equicontinuous semi-locally connected flow. Moreover, we give a sufficient condition of the existence of almost automorphic points, for general flow. We further study equicontinuous local dendrites flows with finitely generated group action. Consequently, we obtain a generalization of Morales’s results in Morales (Topol Appl 198: 101–106, 2016) and Theorem of Su and Qin in Su and Qin (J Differ Equ 25: 1744–1754, 2019).