Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 13, Number 2 (2006), 241-245.
On discontinuous transitive maps and dense orbits
It is well-known that many transitive continuous self-maps have a dense orbit. On the other hand several interesting transitive dynamical systems present some kind of discontinuity. Motivated by a result of A. Peris, we investigate under which conditions a discontinuous transitive map has a dense orbit.
Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 2 (2006), 241-245.
First available in Project Euclid: 19 May 2006
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Primary: 26A18: Iteration [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25] 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.) 54H20: Topological dynamics [See also 28Dxx, 37Bxx] 54E52: Baire category, Baire spaces
Fedeli, Alessandro. On discontinuous transitive maps and dense orbits. Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 2, 241--245. doi:10.36045/bbms/1148059460. https://projecteuclid.org/euclid.bbms/1148059460