# TOTALLY CHAIN-TRANSITIVE ATTRACTORS OF GENERIC HOMEOMORPHISMS ARE PERSISTENT

• 발행 : 2005.08.01

#### 초록

we prove that, given any compact metric space X, there exists a residual subset R of H(X), the space of all homeomorphisms on X, such that if $\in$ R has a totally chain-transitive attractor A, then any g sufficiently close to f has a totally chain transitive attractor A$\_{g}$ which is convergent to A in the Hausdorff topology.

#### 참고문헌

1. F. Abdenur, Attractors of generic diffeomorphisms are persistent, Nonlinearity 16 (2003), 301-311 https://doi.org/10.1088/0951-7715/16/1/318
2. C. Bonatti and S. Crovisier, Recurrence et genericite, preprint.
3. C. Conley, Isolated invariant sets and the Morse index, CBMS Regional Conf. Ser. in Math, vol. 38, Amer. Math. Soc, providence, R. I., 1978
4. M. Hurley, Attractors: Persistence and density of their basins, Trans. Amer. Math. Soc. 269 (1982), 247-271 https://doi.org/10.2307/1998602
5. K. Kuratowski, Topology II, Academic Press-PWN-Polish Sci. Publishers Warszawa, 1968
6. J. Milnor, On the consept of attractors, Interscience, New York, 1957. Comm. Math. Phys. 99 (1986), 177-195 https://doi.org/10.1007/BF01212280

#### 피인용 문헌

1. Chain recurrence rates and topological entropy vol.156, pp.2, 2008, https://doi.org/10.1016/j.topol.2008.07.005