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Periodic Points and Contractive Mappings
Canadian Mathematical Bulletin, 1974Let X be a non-empty set and f:X→X. A point x ∈ X is (i) a fixed point off f(x)=x, and (ii) a periodic point of f iff there is a positive integer N such that fN(x)=x. Also a periodic orbit of f is the (finite) set {x, f(x), f2(x),…} where x is a periodic point of f.
Hsieh, Tsu-Teh, Tan, Kok-Keong
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1980
Now that the notions of ‘point structure’ and ‘period structure’ have been developed to some extent, it becomes of interest to relate the two in a systematic fashion. For this purpose, once more, here are the relevant notions as they evolved in the previous discussions.
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Now that the notions of ‘point structure’ and ‘period structure’ have been developed to some extent, it becomes of interest to relate the two in a systematic fashion. For this purpose, once more, here are the relevant notions as they evolved in the previous discussions.
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Correction to: Fixed point and periodic point theorems
Acta Scientiarum MathematicarumzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pant, R. P., Rakočević, Vladimir
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Communications in Contemporary Mathematics, 2021
We introduce the notion of exotic periodic points of a meromorphic self-map. We then establish the expected asymptotic for the number of isolated or exotic periodic points for holomorphic self-maps with a simple action on the cohomology groups on a compact Kähler manifold.
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We introduce the notion of exotic periodic points of a meromorphic self-map. We then establish the expected asymptotic for the number of isolated or exotic periodic points for holomorphic self-maps with a simple action on the cohomology groups on a compact Kähler manifold.
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Periodic points of polynomials
Ukrainian Mathematical Journal, 1989See the review in Zbl 0686.30019.
Eremenko, A. Eh., Levin, G. M.
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Fixed point and periodic point theorems
Acta Scientiarum Mathematicarum\textit{R. P. Pant} [Bull. Calcutta Math. Soc. 90, No. 4, 281--286 (1998; Zbl 0936.54043)] began research on the properties of mappings weaker than continuity which can ensure the existence of a fixed point. The present paper develops this topic. Unfortunately, the paper contains many editorial imperfections.
Pant, R. P., Rakočević, Vladimir
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Mathematische Annalen, 2001
Let \(M\) be a complete PL manifold and \(f: M\to M\) a map. The Nielsen number \(N(f)\) is a lower bound for the number of fixed points of every map homotopic to \(f\). If the dimension of \(M\) is at least three, then there is a map \(g\) homotopic to \(f\) such that \(g\) has exactly \(N(f)\) fixed points.
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Let \(M\) be a complete PL manifold and \(f: M\to M\) a map. The Nielsen number \(N(f)\) is a lower bound for the number of fixed points of every map homotopic to \(f\). If the dimension of \(M\) is at least three, then there is a map \(g\) homotopic to \(f\) such that \(g\) has exactly \(N(f)\) fixed points.
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