Dynamical Systems on Graph Limits and Their Symmetries

• DOI: 10.48550/arxiv.2110.13686
• Publication Date: 2021-01-01
• Authors: Christian Bick; Davide Sclosa
• Keywords: Equivariant dynamics; 0103 physical sciences; FOS: Mathematics; Graph limits; Network dynamics; Dynamical Systems (math.DS); Mathematics - Dynamical Systems; 0101 mathematics; 01 natural sciences; 37C81, 05C99 (Primary) 37G40 28D15 34C15 (Secondary); Automorphism group

The collective dynamics of interacting dynamical units on a network crucially depends the properties structure. Rather than considering large but finite graphs to capture network, one often resorts graph limits and thereon. We elucidate symmetry systems -- including graphons graphops analyze how shape dynamics, for example through invariant subspaces. In addition traditional symmetries, can support generalized noninvertible symmetries. Moreover, as asymmetric networks have symmetric limits, we note that expect see ghosts symmetries in networks.