SHADOWABLE CHAIN TRANSITIVE SETS OF C1-GENERIC DIFFEOMORPHISMS

C-stably Shadowable Conservative Diffeomorphisms Are Anosov

In this short note we prove that if a symplectomorphism f is C-stably shadowable, then f is Anosov. The same result is obtained for volume-preserving diffeomorphisms.

Sharply $(n-2)$-transitive Sets of Permutations

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...

-generic Diffeomorphisms

On the one hand, we prove that the spaces of C 1 symplectomor-phisms and of C 1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On the other hand, we show that the space of C 1 diffeomorphisms of the circle and a non-empty open set of C 1 diffeomorphisms of the two-sphere contain dense subsets of diffeomorphisms whose centralize...

On transitive soft sets over semihypergroups

The aim of this paper is to initiate and investigate new soft sets over semihypergroups, named special soft sets and transitive soft sets and denoted by $S_{H}$ and  $T_{H},$ respectively. It is shown that $T_{H}=S_{H}$ if and only if $beta=beta^{*}.$ We also introduce the derived semihypergroup from a special soft set and study some properties of this class of semihypergroups.

Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds