wandering continua of Lattes map
نویسندگان
چکیده
In this paper, we study the problem of wandering continua for a Lattes map. For such a map, we prove that it admits a wandering continuum if and only if it is a flexible Lattes map.
منابع مشابه
Exactly two-to-one maps from continua onto some tree-like continua
It is known that no dendrite (Gottschalk 1947) and no hereditarily indecomposable tree-like continuum (J. Heath 1991) can be the image of a continuum under an exactly 2-to-1 (continuous) map. This paper enlarges the class of tree-like continua satisfying this property, namely to include those tree-like continua whose nondegenerate proper subcontinua are arcs. This includes all Knaster continua ...
متن کاملBackward Stability for Polynomial Maps with Locally Connected Julia Sets
We study topological dynamics on unshielded planar continua with weak expanding properties at cycles for which we prove that the absence of wandering continua implies backward stability. Then we deduce from this that a polynomial f with a locally connected Julia set is backward stable outside any neighborhood of its attracting and neutral cycles. For a conformal measure μ this easily implies th...
متن کاملThe Non-wandering Set of a CA Map
An example is given of a cellular automaton map F implementing a binary counter whose non-wandering set , n(F), is st rictly larger than the closure, fI(F ), of the set of points periodic under F.
متن کاملA note on a Whitney map for continua
Let X be a non-metric continuum, and C(X) the hyperspace of subcontinua of X. It is known that there is no Whitney map on the hyperspace 2 for non-metrizable Hausdorff compact spaces X. On the other hand, there exist non-metrizable continua which admit and the ones which do not admit a Whitney map for C(X). In this paper we investigate the properties of non-metrizable continua which admit a Whi...
متن کاملOn Multiply Connected Wandering Domains of Meromorphic Functions
We describe conditions under which a multiply connected wandering domain of a transcendental meromorphic function with a finite number of poles must be a Baker wandering domain, and we discuss the possible eventual connectivity of Fatou components of transcendental meromorphic functions. We also show that if f is meromorphic, U is a bounded component of F (f) and V is the component of F (f) suc...
متن کامل