Sensitive actions in non-compact spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913957355192320 |
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| author | Portela, Jorge Iglesias Aldo |
| author_facet | Portela, Jorge Iglesias Aldo |
| contents | Devaney defines a function as chaotic if it satisfies the following three conditions: transitivity, having a dense set of periodic points, and sensitive dependence on initial conditions. In \cite{3}, it was demonstrated that the first two conditions imply the third. This result was generalized in \cite{aak} by replacing the density of periodic points with the density of minimal points. The result was further generalized in \cite{g} for group actions, in \cite{km} for $C$-semigroups actions, and in \cite{d} for a continuous semi-flow with $X$ being a Polish space. Subsequently, in \cite{ip1} and \cite{ip2}, it was generalized for compact spaces and for non-compact spaces in \cite{z}. The objective of this work is to generalize the result in \cite{z}, providing a simple proof. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_12323 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sensitive actions in non-compact spaces Portela, Jorge Iglesias Aldo Dynamical Systems Primary: 37B05, Secondary: 20M30 Devaney defines a function as chaotic if it satisfies the following three conditions: transitivity, having a dense set of periodic points, and sensitive dependence on initial conditions. In \cite{3}, it was demonstrated that the first two conditions imply the third. This result was generalized in \cite{aak} by replacing the density of periodic points with the density of minimal points. The result was further generalized in \cite{g} for group actions, in \cite{km} for $C$-semigroups actions, and in \cite{d} for a continuous semi-flow with $X$ being a Polish space. Subsequently, in \cite{ip1} and \cite{ip2}, it was generalized for compact spaces and for non-compact spaces in \cite{z}. The objective of this work is to generalize the result in \cite{z}, providing a simple proof. |
| title | Sensitive actions in non-compact spaces |
| topic | Dynamical Systems Primary: 37B05, Secondary: 20M30 |
| url | https://arxiv.org/abs/2405.12323 |