TOTALLY CHAIN-TRANSITIVE ATTRACTORS OF GENERIC HOMEOMORPHISMS ARE PERSISTENT

Title & Authors
TOTALLY CHAIN-TRANSITIVE ATTRACTORS OF GENERIC HOMEOMORPHISMS ARE PERSISTENT
GHANE FATEMEH HELEN; FAKHARI ABBAS;

Abstract
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 $\small{\in}$ R has a totally chain-transitive attractor A, then any g sufficiently close to f has a totally chain transitive attractor A$\small{\_{g}}$ which is convergent to A in the Hausdorff topology.
Keywords
totally chain-transitive;attractor;persistent;
Language
English
Cited by
1.
Chain recurrence rates and topological entropy, Topology and its Applications, 2008, 156, 2, 251
References
1.
F. Abdenur, Attractors of generic diffeomorphisms are persistent, Nonlinearity 16 (2003), 301-311

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

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