منابع مشابه
Measure Preserving Homeomorphisms at Fixed Points
In an article of a few years ago [2] Kerékjartó obtained interesting results about certain types of transformations which he called similitudes. With a few modifications and extensions his methods can be used to gain information about the structure of measure preserving transformations at fixed points. For simplicity the results are formulated for Euclidean w-space although they could easily be...
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We show that, for any n ≠ 2, most orientation preserving homeomorphisms of the sphere S2n have a Cantor set of fixed points. In other words, the set of such homeomorphisms that do not have a Cantor set of fixed points is of the first Baire category within the set of all homeomorphisms. Similarly, most orientation reversing homeomorphisms of the sphere S2n+1 have a Cantor set of fixed points for...
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Michael Handel proved in [7] the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links at infinity. More recently, the author generalized Handel’s theorem to a wider class of cycles of links [13]. In this paper we complete this topic describing...
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Nielsen fixed point theory (see [1, 4]) deals with the estimation of the number of fixed points of maps in the homotopy class of any given map f : X → X . The Nielsen number N( f ) provides a lower bound. A classical result in Nielsen fixed point theory is: any map f : X → X is homotopic to a map with exactly N( f ) fixed points if the compact polyhedron X has no local cut point and is not a 2-...
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An orientation-preserving recurrent homeomorphism of the twosphere which is not the identity is shown to admit exactly two fixed points. A recurrent homeomorphism of a compact surface with negative Euler characteristic is periodic.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1981
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1981-14937-5