منابع مشابه
Certain Homogeneous Unicoherent Indecomposable Continua
A simple closed curve is the simplest example of a compact, nondegenerate, homogeneous continuum. If a bounded, nondegenerate, homogeneous plane continuum has any local connectedness property, even of the weakest sort, it is known to be a simple closed curve [l, 2, 3].1 The recent discovery of a bounded, nondegenerate, homogenous plane continuum which does not separate the plane [4, 5] has give...
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In this paper we prove the existence of uncountably many indecomposable continua in the dynamics of complex exponentials of the form Eλ(z) = λe z with λ > 1/e. These continua contain points that share the same itinerary under iteration of Eλ. These itineraries are bounded but consist of blocks of 0’s whose lengths increase, and hence these continua are never periodic.
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Let X be a Hausdorff continuum (a compact connected Hausdorff space). Let 2X (respectively, Cn(X)) denote the hyperspace of nonempty closed subsets of X (respectively, nonempty closed subsets of X with at most n components), with the Vietoris topology. We prove that if X is hereditarily indecomposable, Y is a Hausdorff continuum and 2X (respectively Cn(X)) is homeomorphic to 2Y (respectively, C...
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Swingle [7]1 has given the following definitions. (1) A continuum M is said to be the finished sum of the continua of a collection G if G* = M and no continuum of G is a subset of the sum of the others.2 (2) If » is a positive integer, the continuum M is said to be indecomposable under index » if If is the finished sum of « continua and is not the finished sum of »+1 continua. Swingle has shown...
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In this paper we describe several new types of invariant sets that appear in the Julia sets of the complex exponential functions Eλ(z) = λe z where λ ∈ C. These invariant sets consist of points that share the same itinerary under iteration of Eλ. Since these exponential functions are 2πi periodic, there are several “natural” ways (described below) to decompose the plane into countably many stri...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1976
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1976.62.587