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Symmetry 2018, 10(6), 211; https://doi.org/10.3390/sym10060211

Dynamics on Binary Relations over Topological Spaces

1
Department of Mathematics Education, National Taichung University of Education, Taichung 403, Taiwan
2
Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, E-46022 València, Spain
3
Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
4
Departamento de Matemáticas, Universitat Jaume I, Campus de Ríu Sec, E-12071 Castelló de la Plana, Spain
*
Author to whom correspondence should be addressed.
Received: 16 April 2018 / Revised: 4 June 2018 / Accepted: 7 June 2018 / Published: 11 June 2018
(This article belongs to the Special Issue Symmetry in Graph Theory)
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Abstract

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. View Full-Text
Keywords: Devaney chaos; hypercyclicity; topological transitivity; topologically mixing; disjointness; connectivity Devaney chaos; hypercyclicity; topological transitivity; topologically mixing; disjointness; connectivity
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Chen, C.-C.; Conejero, J.A.; Kostić, M.; Murillo-Arcila, M. Dynamics on Binary Relations over Topological Spaces. Symmetry 2018, 10, 211.

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