Topological dynamics on hyperspaces
In this paper we wish to relate the dynamics of the base map to the dynamics of the induced map. In the process, we obtain conditions on the endowed hyperspace topology under which the chaotic behaviour of the map on the base space is inherited by the induced map on the hyperspace. Several of the kn...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2010-04-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1724 |
| _version_ | 1819084600610127872 |
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| author | Puneet Sharma Anima Nagar |
| author_facet | Puneet Sharma Anima Nagar |
| author_sort | Puneet Sharma |
| collection | DOAJ |
| description | In this paper we wish to relate the dynamics of the base map to the dynamics of the induced map. In the process, we obtain conditions on the endowed hyperspace topology under which the chaotic behaviour of the map on the base space is inherited by the induced map on the hyperspace. Several of the known results come up as corollaries to our results. We also discuss some metric related dynamical properties on the hyperspace that cannot be deduced for the base dynamics. |
| first_indexed | 2024-12-21T20:51:02Z |
| format | Article |
| id | doaj.art-7cc22a2495394fc2b3b1c121cacb69b3 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-21T20:51:02Z |
| publishDate | 2010-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-7cc22a2495394fc2b3b1c121cacb69b32022-12-21T18:50:42ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472010-04-0111111910.4995/agt.2010.17241412Topological dynamics on hyperspacesPuneet Sharma0Anima Nagar1Indian Institute of Technology DelhiIndian Institute of Technology DelhiIn this paper we wish to relate the dynamics of the base map to the dynamics of the induced map. In the process, we obtain conditions on the endowed hyperspace topology under which the chaotic behaviour of the map on the base space is inherited by the induced map on the hyperspace. Several of the known results come up as corollaries to our results. We also discuss some metric related dynamical properties on the hyperspace that cannot be deduced for the base dynamics.http://polipapers.upv.es/index.php/AGT/article/view/1724HyperspaceHit and miss topologyHit and far-miss topologyInduced mapTransitivityMixingHorseshoeEquicontinuityScrambled set |
| spellingShingle | Puneet Sharma Anima Nagar Topological dynamics on hyperspaces Applied General Topology Hyperspace Hit and miss topology Hit and far-miss topology Induced map Transitivity Mixing Horseshoe Equicontinuity Scrambled set |
| title | Topological dynamics on hyperspaces |
| title_full | Topological dynamics on hyperspaces |
| title_fullStr | Topological dynamics on hyperspaces |
| title_full_unstemmed | Topological dynamics on hyperspaces |
| title_short | Topological dynamics on hyperspaces |
| title_sort | topological dynamics on hyperspaces |
| topic | Hyperspace Hit and miss topology Hit and far-miss topology Induced map Transitivity Mixing Horseshoe Equicontinuity Scrambled set |
| url | http://polipapers.upv.es/index.php/AGT/article/view/1724 |
| work_keys_str_mv | AT puneetsharma topologicaldynamicsonhyperspaces AT animanagar topologicaldynamicsonhyperspaces |