| Abstract: |
| This talk is based on a series of papers (mentioned below), which aim at studying the sets of periodic points of automorphisms on a solenoid. In these papers, we attempted to characterise the sets of periodic points of solenoidal automorphisms. In [1], we characterized the sets of periodic points of 1-dimensional solenoids and full solenoids. In the next paper [2], it was extended to some higher dimensional solenoids in terms of inverse limits of certain maps on a torus. Finally, the third paper [3] does this using the concept of adeles. The talk starts with an introduction to some basic notions of topological dynamics that are required to present our results, followed by a summary of the results mentioned above. It is then concluded with the same question for more general dynamical systems than solenoids.
[1] Gopal, Sharan and Raja, C.R.E. \textit{Periodic points of solenoidal automorphisms}, Topology Proceedings, 50 (2017), 49-57.
[2] Gopal, Sharan and Imam, Faiz. \textit{Periodic points of solenoidal automorphisms in terms of inverse limits}, Appl. Gen. Topology, Vol. 22 (2021), 321-330.
[3] Imam, Faiz and Gopal, Sharan. \textit{Periodic points of solenoidal automorphisms in terms of adeles}, Monatsh Math 204 (2024), 501-511. |
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