منابع مشابه
On Finite-to-one Maps
Let f : X → Y be a σ-perfect k-dimensional surjective map of metrizable spaces such that dimY ≤ m. It is shown that, for every integer p ≥ 1 there exists a dense Gδ-subset H(k,m, p) of C(X, I k+p ) with the source limitation topology such that each fiber of f△g, g ∈ H(k,m, p), contains at most max{k+m−p+2, 1} points. This result provides a proof of Hypothesis 1 and Hypothesis 2 from [1].
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It is a fundamental fact about simultaneous linear equations that uniqueness implies existence in the sense that if the »X» system MX= Y has, for each Y, at most one solution X, then, for each Y, the equation actually has a solution. Our purpose is to show that this situation persists for certain "nonlinear equations" as well, namely that, restricting everything to the reals, if Pi, P2 are poly...
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To Ken Kunen on the occasion of his retirement from teaching MSC: primary 54F45 secondary 54C10, 54G05
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Some techniques and results in the renormalization theory of real and complex dynamical systems are summarized. The construction of the induced Markov map of [−1, 1] from a Feigenbaum-like map is presented. We show that this induced Markov map has bounded geometry. We discuss some property of infinitely renormalizable quadratic polynomials and show that the Julia set of an infinitely renormaliz...
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Skinning maps were introduced by William Thurston in the proof of the Geometrization Theorem for Haken 3-manifolds (see [Ota]). At a key step in the proof one has a compact 3-manifold M with nonempty boundary whose interior admits a hyperbolic structure. The interplay between deformations of the hyperbolic structure and the topology of M and ∂M determines a holomorphic map of Teichmüller spaces...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2006
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-06-03922-5