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math.DS2026
Transfinite Topological Dynamics
Alessandro Della Corte, Marco Farotti
We present a canonical extension of topological dynamics to transfinite iterations, which makes precise the idea of dynamical phenomena stabilizing at different time-scales. Specif…
math.DS2026
Chains without regularity
Alessandro Della Corte, Marco Farotti
We study chain-recurrence and chain-transitivity in compact dynamical systems without any regularity assumptions on the map. We prove that every compact system has a chain-recurren…
math.DS2026
Order spectra in topological dynamical systems
F. Ciavattini, A. Della Corte, C. Lucamarini
In a compact topological dynamical system , we associate to every pair a canonical order-theoretic invariant, its emergent order spectrum . We first prove th…