{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T22:48:26Z","timestamp":1772664506152,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,11]],"date-time":"2018-06-11T00:00:00Z","timestamp":1528675200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003176","name":"Ministerio de Educaci\u00f3n, Cultura y Deporte","doi-asserted-by":"publisher","award":["MTM2016-75963-P"],"award-info":[{"award-number":["MTM2016-75963-P"]}],"id":[{"id":"10.13039\/501100003176","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The existence of chaos and the quest of dense orbits have been recently considered for dynamical systems given by multivalued linear operators. We consider the notions of topological transitivity, topologically mixing property, hypercyclicity, periodic points, and Devaney chaos in the general case of binary relations on topological spaces, and we analyze how they can be particularized when they are represented with graphs and digraphs. The relations of these notions with different types of connectivity and with the existence of Hamiltonian paths are also exposed. Special attention is given to the study of dynamics over tournaments. Finally, we also show how disjointness can be introduced in this setting.<\/jats:p>","DOI":"10.3390\/sym10060211","type":"journal-article","created":{"date-parts":[[2018,6,11]],"date-time":"2018-06-11T11:01:01Z","timestamp":1528714861000},"page":"211","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Dynamics on Binary Relations over Topological Spaces"],"prefix":"10.3390","volume":"10","author":[{"given":"Chung-Chuan","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Mathematics Education, National Taichung University of Education, Taichung 403, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3681-7533","authenticated-orcid":false,"given":"J. Alberto","family":"Conejero","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, E-46022 Val\u00e8ncia, Spain"}]},{"given":"Marko","family":"Kosti\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovi\u0107a 6, 21125 Novi Sad, Serbia"}]},{"given":"Marina","family":"Murillo-Arcila","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universitat Jaume I, Campus de R\u00edu Sec, E-12071 Castell\u00f3 de la Plana, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,11]]},"reference":[{"key":"ref_1","unstructured":"Strogatz, S.H. (1994). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity). 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