Geodesic
Limit Sets of Typical Homeomorphisms
Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 225-232

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

Given an integer $n\,\ge \,3$ , a metrizable compact topological $n$ -manifold $X$ with boundary, and a finite positive Borel measure $\mu $ on $X$ , we prove that for the typical homeomorphism $f\,:\,X\,\to \,X$ , it is true that for $\mu $ -almost every point $x$ in $X$ the limit set $\omega (f,\,x)$ is a Cantor set of Hausdorff dimension zero, each point of $\omega (f,\,x)$ has a dense orbit in $\omega (f,\,x)$ , $f$ is non-sensitive at each point of $\omega (f,\,x)$ , and the function $a\,\to \,\omega (f,\,a)$ is continuous at $x$ .
DOI : 10.4153/CMB-2011-066-2
Mots-clés : 37B20, 54H20, 28C15, 54C35, 54E52, topological manifolds, homeomorphisms, measures, Baire category, limit sets 
Jr., Nilson C. Bernardes. Limit Sets of Typical Homeomorphisms. Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 225-232. doi: 10.4153/CMB-2011-066-2
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[1] [1] Agronsky, S. J., Bruckner, A. M., and Laczkovich, M., Dynamics of typical continuous functions. J. London Math. Soc. (2) 40(1989), no. 2, 227–243. Google Scholar | DOI

[2] [2] Akin, E., On chain continuity. Discrete Contin. Dynam. Systems 2(1996), no. 1, 111–120. Google Scholar | DOI

[3] [3] Akin, E., Hurley, M., and Kennedy, J. A., Dynamics of topologically generic homeomorphisms. Mem. Amer. Math. Soc. 164(2003), no. 783. Google Scholar

[4] [4] Bernardes, N. C. Jr., On the predictability of discrete dynamical systems. Proc. Amer. Math. Soc. 130(2002), no. 7, 1983–1992. Google Scholar | DOI

[5] [5] Bernardes, N. C. Jr., On the predictability of discrete dynamical systems. II. Proc. Amer. Math. Soc. 133(2005), no. 12, 3473–3483. Google Scholar | DOI

[6] [6] Bernardes, N. C. Jr., Limit sets of typical continuous functions. J. Math. Anal. Appl. 319(2006), no. 2, 651–659. Google Scholar | DOI

[7] Bernardes, N. C. Jr., On the predictability of discrete dynamical systems. III. J. Math. Anal. Appl. 339(2008), no. 1, 58–69. Google Scholar | DOI

[8] [8] Diestel, R., Graph theory. Graduate Texts in Mathematics, 173, Springer-Verlag, New York, 1997. Google Scholar

[9] [9] Lehning, H., Dynamics of typical continuous functions. Proc. Amer. Math. Soc. 123(1995), no. 6, 1703–1707. Google Scholar

[10] [10] Munkres, J. R., Elements of algebraic topology. Addison-Wesley Publishing Company, Menlo Park, CA, 1984. Google Scholar

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