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- W2895918878 abstract "The expansive map and chaos have an important significance in terms of theory and application. According to the definition of expansive map and chaos, we give the concept of G-expansive map and Devaney's G-Chaos in this paper. By inference, some conclusions of the metric space were extended to the metric G-space. We have the following result:(1) Let X be a metric G-space, G be a commutative topological group and f be a equivariant self-map on X .Then we have that the map f satisfies the first condition and second condition of Devaney's G-Chaos if and only if the sets U and V have the same periodic orbit where U and V be any nonempty open sets; (2) Let X be a metric G-space and f be a homeomorphism map of X into itself. Then we have that f is a G-expansive map if and only if f^m is a Gexpansive map for any nonzero integer m; (3) Let (X,d_1) and (Y,d_2 ) be a metric G-space. Let f be a homeomorphism and equivariant map from X to Y. If h is a G-expansive map of X into itself, then fhf^-11 is a Gexpansive map of Y into itself; (4) Let X be a metric G-space, A be a invariant subset of G and X X-A be finite. Let f be a homeomorphism map on X. If f is G-expansive on A, then f is G-expansive on X; (5) Let X be a compact metric G-space and G be compact. If f is a G-expansive map with G-expansive constant I´, then for each Iµ > 0 satifying 0 I´ for some integer n where |n| <T≤ k. These results enriched the theory of the G-expansive map and Devaney's G-Chaos." @default.
- W2895918878 created "2018-10-26" @default.
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- W2895918878 date "2018-06-01" @default.
- W2895918878 modified "2023-09-25" @default.
- W2895918878 title "The Research of G- expansive Map and Devaney’s G-Chaos Condition on Metric G-Space" @default.
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- W2895918878 doi "https://doi.org/10.1109/icsgea.2018.00066" @default.
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