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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2601.21888 |
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| _version_ | 1866917232640000000 |
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| author | Fel'shtyn, Alexander Slomiany, Mateusz |
| author_facet | Fel'shtyn, Alexander Slomiany, Mateusz |
| contents | In this paper, we introduce the synchronization zeta function associated with a pair of self-maps of a topological space and investigate its properties. We also define the growth rate of synchronization points and derive an explicit formula in the setting of endomorphisms of compact, connected Abelian groups. In addition, we establish Gauss congruences and describe the asymptotic behavior for the sequence of numbers of synchronization points, under the assumption that the synchronization zeta function is rational. Further, we discuss connections with topological entropy and Reidemeister torsion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21888 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Synchronization points: growth, asymptotics, congruences, and the synchronization zeta function Fel'shtyn, Alexander Slomiany, Mateusz Dynamical Systems Mathematical Physics Algebraic Topology Group Theory Representation Theory 37C25, 37C30, 22D10 In this paper, we introduce the synchronization zeta function associated with a pair of self-maps of a topological space and investigate its properties. We also define the growth rate of synchronization points and derive an explicit formula in the setting of endomorphisms of compact, connected Abelian groups. In addition, we establish Gauss congruences and describe the asymptotic behavior for the sequence of numbers of synchronization points, under the assumption that the synchronization zeta function is rational. Further, we discuss connections with topological entropy and Reidemeister torsion. |
| title | Synchronization points: growth, asymptotics, congruences, and the synchronization zeta function |
| topic | Dynamical Systems Mathematical Physics Algebraic Topology Group Theory Representation Theory 37C25, 37C30, 22D10 |
| url | https://arxiv.org/abs/2601.21888 |