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math.DS2025
On linearly ordered sets of chain components
P. Cintioli, A. Della Corte, M. Farotti
In a dynamical system , with a compact metric space, the chain components, the fundamental building blocks in the Conley decomposition of dynamics, have a natural partia…
math.DS2025
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.DS2025
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…