The respected Comrade
"The basic sciences are the cornerstone of a sci-tech power. A high level of basic sciences enables a country's science and technology to make steady progress on a solid foundation."
We studied the chaotic properties of topological dynamical system via Furstenberg family.
Recently, some scholars investigated the basic concepts of topological dynamical system such as sensitivity, transitivity, equicontinuity via Furstenberg family.
For the chaotic properties of dynamical systems via Furstenberg family, the relationship between the basic system and the induced system and also the interrelationship between the chaotic properties via Furstenberg family have been studied. The relevant literature tells us that there are various notions about sensitivity and those are not equivalent in general, and we discussed the condition under which those are equivalent. We submitted the obtained result in an article entitled "About two definitions of F-sensitivity" (https://doi.org/10.1016/j.topol.2019.106927) was published in "Topology and its Applications".(269(2020) 106927)
And we generalized the relationship between sensitivity and equicontinuity, which is known as the classical result in the theory of topological dynamical system, by using Furstenberg family. And we also submitted the obtained result in an article entitled "F-equicontinuity and an analogue of Auslander-Yorke dichotomy theorem" (https://doi.org/10.1016/j.topol.2020.107252) was published in "Topology and its Applications".