Geodesic
On Irregular Fixed Points
Canadian mathematical bulletin, Tome 10 (1967) no. 4, pp. 507-512

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout this paper (X, d) will be a metric space with metric d, and h ahomeomorphism of X onto itself. For any real number r > 0, and p ∊ X,U(p, r) will denote the open r - sphere about p. Any point p ∊ X is calledregular [3] if for any given ∊ > 0 there exists a δ > 0 such that d(p,y) <δ implies d(hn(p), hn(y)) < ∊ for allintegers n, where hn denotes the iterates of h for n > 0, of h-1 for n < 0, and h0 is the identity. Any pointof X which is not a regular point i s called an irregular point. Let I(h)denote the set of all the irregular points of X and R(h) = X-I(h). Lim infand Lim sup are defined as in [4]. 
Kaul, S.K. On Irregular Fixed Points. Canadian mathematical bulletin, Tome 10 (1967) no. 4, pp. 507-512. doi: 10.4153/CMB-1967-049-6
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[1] 1. Homma, T. and Kinoshita, S., On homeomorphisms which are regular except for a finite number of points. Osaka Math. Jour. 7 (1955), p. 29-38. Google Scholar

[2] 2. Kaul, S. K., On almost regular homeomorphisms. To be published in Canadian Journal of Math. Google Scholar

[3] 3. Kerèkjártó, B. v., Topologische charakterisierung der linearen Abbildungen. Acta. litt. ac. Sci., Szeged, 6(1933), p. 235-62. Google Scholar

[4] 4. Whyburn, G. T., Analytic Topology. Amer. Math. Soc. Coll. Publ, 1942. Google Scholar

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