WIAS Preprint No. 3092, (2024)

Time-periodic behaviour in one- and two-dimensional interacting particle systems


  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Köppl, Jonas
    ORCID: 0000-0001-9188-1883

2020 Mathematics Subject Classification

  • 60K35 60K35


  • Interacting particle systems, Gibbs measures, periodic behaviour, attractor properties, synchronisation, non-ergodicity, non-equilibrium stationary state




We provide a class of examples of interacting particle systems on $Z^d$, for $din1,2$, that admit a unique translation-invariant stationary measure, which is not the long-time limit of all translation-invariant starting measures, due to the existence of time-periodic orbits in the associated measure-valued dynamics. This is the first such example and shows that even in low dimensions, not every limit point of the measure-valued dynamics needs to be a time-stationary measure.

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