T . Sun , H . Xi and X . Peng A NOTE ON ω - LIMIT SET OF A TREE MAP
نویسنده
چکیده
Let T be a tree and f : T → T be continuous. Denote by P (f) and ω(x, f) the set of periodic points of f and ω-limit set of x under f respectively. Write Λ(f) = ⋃ x∈T ω(x, f). In this paper, we show that if x ∈ Λ(f)−P (f), then ω(x, f) is an infinite minimal set.
منابع مشابه
The 2-dimension of a Tree
Let $x$ and $y$ be two distinct vertices in a connected graph $G$. The $x,y$-location of a vertex $w$ is the ordered pair of distances from $w$ to $x$ and $y$, that is, the ordered pair $(d(x,w), d(y,w))$. A set of vertices $W$ in $G$ is $x,y$-located if any two vertices in $W$ have distinct $x,y$-location.A set $W$ of vertices in $G$ is 2-located if it is $x,y$-located, for some distinct...
متن کاملOn Open Maps between Dendrites
In this paper we use a result by J. Krasinkiewicz to present a description of the topological behavior of an open map defined between dendrites. It is shown that, for every such map f : X → Y, there exist n subcontinua X1, X2,. . ., Xn of X such that X = X1∪X2∪· · ·∪Xn, each set Xi∩Xj consists of at most one element which is a critical point of f , and each map f|Xi : Xi → Y is open, onto and c...
متن کاملω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS
Abstract. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also le...
متن کامل(Non)invertibility of Fibonacci-like unimodal maps restricted to their critical omega-limit sets
A Fibonacci(-like) unimodal map is defined by special combinatorial properties which guarantee that the critical omega-limit set ω(c) is a minimal Cantor set. In this paper we give conditions to ensure that f |ω(c) is invertible, except at a subset of the backward critical orbit. Furthermore, any finite subtree of the binary tree can appear for some f as the tree connecting all points at which ...
متن کاملLecture 4: Symplectic Group Actions
We set S1 = R/2πZ throughout. Let (M,ω) be a symplectic manifold. A symplectic S1-action on (M,ω) is a smooth family ψt ∈ Symp(M,ω), t ∈ S1, such that ψt+s = ψt ◦ ψs for any t, s ∈ S1. One can easily check that the corresponding vector fields Xt ≡ d dtψt ◦ψ −1 t is time-independent, i.e., Xt = X is constant in t. We call X the associated vector field of the given symplectic S1-action. Note that...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011