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In [Ko\u010dan et al., 2014] we consider six such properties and survey the relations among them for the cases of graph maps, dendrite maps and maps on compact metric spaces. <\/jats:p><jats:p> In this paper, we consider fourteen such properties, provide new results and survey all the relations among the properties for the case of graph maps and all known relations for the case of dendrite maps. We formulate some open problems at the end of the paper. <\/jats:p>","DOI":"10.1142\/s0218127421501005","type":"journal-article","created":{"date-parts":[[2021,6,18]],"date-time":"2021-06-18T04:18:28Z","timestamp":1623989908000},"page":"2150100","source":"Crossref","is-referenced-by-count":2,"title":["Properties of Dynamical Systems on Dendrites and Graphs"],"prefix":"10.1142","volume":"31","author":[{"given":"Zden\u011bk","family":"Ko\u010dan","sequence":"first","affiliation":[{"name":"Mathematical Institute in Opava, Silesian University in Opava, Na Rybn\u00ed\u010dku 1, 746 01 OPAVA, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Veronika","family":"Kurkov\u00e1","sequence":"additional","affiliation":[{"name":"Mathematical Institute in Opava, Silesian University in Opava, Na Rybn\u00ed\u010dku 1, 746 01 OPAVA, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michal","family":"M\u00e1lek","sequence":"additional","affiliation":[{"name":"Mathematical Institute in Opava, Silesian University in Opava, Na Rybn\u00ed\u010dku 1, 746 01 OPAVA, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2021,6,18]]},"reference":[{"key":"S0218127421501005BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/1980"},{"key":"S0218127421501005BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2010.10.040"},{"key":"S0218127421501005BIB003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1978-0509258-X"},{"key":"S0218127421501005BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0086977"},{"key":"S0218127421501005BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0084762"},{"key":"S0218127421501005BIB007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1971-0274707-X"},{"key":"S0218127421501005BIB008","doi-asserted-by":"publisher","DOI":"10.1515\/9783110342406"},{"key":"S0218127421501005BIB009","first-page":"19","volume":"190","author":"Dinaburg E.I.","year":"1970","journal-title":"Dokl. 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