DCDS
Pseudo-orbit shadowing in the $C^1$ topology
Flavio Abdenur Lorenzo J. Díaz
Discrete & Continuous Dynamical Systems - A 2007, 17(2): 223-245 doi: 10.3934/dcds.2007.17.223
We prove that the shadowing property does not hold for diffeomorphisms in an open and dense subset of the set of $C^1$-robustly non-hyperbolic transitive diffeomorphisms (i.e., diffeomorphisms with a $C^1$-neighborhood consisting of non-hyperbolic transitive diffeomorphisms).
keywords: Heterodimensional cycle Periodic point Transitivity. Index Pseudo-orbit Shadowing Homoclinic class

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