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Topological dynamics and chaos on compact metric spaces

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Making sense of chaotic phenomena

An EU-funded research initiative supported researcher-directed study of topological dynamics and distributional chaos. Various project successes contributed to advances in this scientific area.

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The 'Topological dynamics and chaos on compact metric spaces' (TOPDS) project had as its scientific focus the study of distributional chaos and its relations to other notions of topological dynamics. The goal was to extend knowledge about chaotic phenomena in dynamical systems, and at the same time to expand the knowledge and research experience of the researcher. Over the course of the project, the researcher achieved a number of successful results, which were to be presented at international meetings. He was also tasked with extending scientific collaborations and starting on new independent lines of research. The technique used to prove that it is possible to transfer a distributionally scrambled set from factor to extension was also used to investigate the dynamics of non-autonomous differential equations. Other TOPDS successes include the development of a formal method of measuring complexity of these equations which, in this context, provided a strict edge between chaotic and non-chaotic dynamics. Activities also resulted in delivery of a method for constructing continuous maps and obtaining elementary proofs relevant to dense periodicity for maps on topological graphs and on specific spaces.

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