In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chao...

A graph $Gamma$ is said to be vertex-transitive or edge‎- ‎transitive‎ ‎if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$‎, ‎respectively‎. ‎Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$‎. ‎Then, $Gamma$ is said to be normal edge-transitive‎, ‎if $N_{Aut(Gamma)}(G)$ acts transitively on edges‎. ‎In this paper‎, ‎the eigenvalues of normal edge-tra...

Let f:X?X be a continuous map on compact metric space X and let ?f, ?f ICTf denote the set of ?-limit sets, ?-limit sets nonempty closed internally chain transitive respectively. In this paper we characterise, by introducing novel variants shadowing, maps for which every element is equal to (resp. may approximated by) same full trajectory. We construct examples highlighting difference between t...

for two normal edge-transitive cayley graphs on groups h and k which have no common direct factor and gcd(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

We consider skew metrics (equivalently, transitive relations that are tournaments, linear orderings) valued in Sugihara semigroups on autodual chains. prove that, for odd chains and without a unit, classify certain tree-like structures we call perfect augmented plane towers. When the chain is finite has cardinality \(2K+1\), set X give rise to rooted trees of height K whose frontier preorder X.

Let $S_n$ be the symmetric group on the set $[n]={1, 2, ldots, n}$. For $gin S_n$ let $fix(g)$ denote the number of fixed points of $g$. A subset $S$ of $S_n$ is called $t$-emph{transitive} if for any two $t$-tuples $(x_1,x_2,ldots,x_t)$ and $(y_1,y_2,ldots ,y_t)$ of distinct elements of $[n]$, there exists $gin S$ such that $x_{i}^g=y_{i}$ for any $1leq ileq t$ and additionally $S$ is called e...

For groups of automorphisms of chains (linear orders) and circles which satisfy certain weak transitivity hypotheses, the Dedekind completion of the chain or circle can be reconstructed up to reversal of order or orientation from the group alone. Let 〈L,<〉 be a dense chain. Throughout, an interval means a nonempty open interval. A subgroup G ≤ Aut(〈L,<〉) is locally moving if for every interval ...

1 Motivations Example 1.1. Let D be a closed subset of R n. We consider the nonau-tonomous ordinary differential system: dx dt = f (t, x), t ≥ 0, x(0) = x 0 ∈ D. Assume that lim t→∞ f (t, x) = f 0 (x) uniformly for x in any bounded subset of D. Then we have a limiting autonomous system: dx dt = f 0 (x), t ≥ 0, x(0) = x 0 ∈ D. Problem. Under what conditions can we lift the long-time properties o...