7,090 research outputs found
Uniform disconnectedness and Quasi-Assouad Dimension
The uniform disconnectedness is an important invariant property under
bi-Lipschitz mapping, and the Assouad dimension implies the
uniform disconnectedness of . According to quasi-Lipschitz mapping, we
introduce the quasi-Assouad dimension such that
implies its quasi uniform disconnectedness. We obtain and compute the quasi-Assouad dimension
of Moran set
On multi-transitivity with respect to a vector
A topological dynamical system is said to be multi-transitive if for
every the system is transitive. We introduce the concept of multi-transitivity with
respect to a vector and show that multi-transitivity can be characterized by
the hitting time sets of open sets, answering a question proposed by Kwietniak
and Oprocha [On weak mixing, minimality and weak disjointness of all iterates,
Erg. Th. Dynam. Syst., 32 (2012), 1661--1672]. We also show that
multi-transitive systems are Li-Yorke chaotic.Comment: 11 page
- …