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Tolerance stability conjecture revisited. (English) Zbl 1024.37012
The author investigates the strong tolerance stability of homeomorphisms (discrete dynamical systems) of a compact smooth manifold. The author proves that the strong tolerance stability property is generic in the space of all homeomorphisms of a compact smooth manifold with \(C^0\) topology.

MSC:
37C20 Generic properties, structural stability of dynamical systems
37C75 Stability theory for smooth dynamical systems
37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics
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[1] E. Akin, M. Hurley, J.A. Kennedy, Dynamics of topologically generic homeomorphisms, Mem. Amer. Math. Soc., to appear · Zbl 1022.37010
[2] Coven, E.M.; Madden, J.; Nitecki, Z., A note on generic properties of continuous maps, (), 97-101
[3] Daszkiewicz, P., A note on tolerance stable dynamical systems, Coll. math., 67, 69-72, (1994) · Zbl 0814.34037
[4] Hurley, M., On proofs of the C0 general density theorem, Proc. amer. math. soc., 124, 1305-1309, (1996) · Zbl 0854.54037
[5] Hurley, M., Properties of attractors of generic homeomorphisms, Ergodic theory dynamical systems, 16, 1297-1310, (1996) · Zbl 0869.58033
[6] Kim, J.-M.; Kye, Y.-H.; Lee, K.-H., Genericity of C stability in dynamical systems, Far east J. math. sci., 1, 191-200, (1993) · Zbl 0798.54048
[7] M. Mazur, C0 generic properties and asymptotic behavior of discrete dynamical systems, Ph.D. Thesis, Institute of Mathematics, Jagiellonian University, Kraków, 2001 (in Polish)
[8] Odani, K., Generic homeomorphisms have the pseudo-orbit tracing property, Proc. amer. math. soc., 110, 281-284, (1990) · Zbl 0713.58025
[9] Ombach, J.; Mazur, M., Shadowing and likes as C0 generic properties, (), 159-168 · Zbl 1083.37021
[10] Palis, J.; Pugh, C.; Shub, M.; Sullivan, D., Genericity theorems in topological dynamics, (), 241-250 · Zbl 0341.54053
[11] Pilyugin, S.Yu., Chain prolongations in typical dynamical systems, Differentsial’nye uravneniya, 26, 1334-1337, (1990), in Russian · Zbl 0713.58021
[12] Pilyugin, S.Yu.; Plamenevskaya, O.B., Shadowing is generic, Topology appl., 97, 253-266, (1999) · Zbl 0973.54035
[13] Takens, F., On Zeeman’s tolerance stability conjecture, (), 209-219 · Zbl 0217.48303
[14] Takens, F., Tolerance stability, (), 293-304 · Zbl 0217.48303
[15] White, W., On the tolerance stability conjecture, (), 663-665
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