Fixed Energy Sandpile and Discrete Harmonicity
نویسنده
چکیده
The Fixed Energy Sandpile with the deterministic Bak-Tang-Wiesenfeld rule on the two-dimensional torus, is studied in order to characterize existence and growth rate of the basins of periodic avalanches. The link between discrete harmonicity and invariant quantities, or toppling invariants, is shown. For an important subclass, these invariants are proven to be related to discrete harmonic polynomials, and such a relation is explored in detail. A notion of independence is introduced to extract effective invariants from the redundant set of all conserved quantities. We discuss how the partition induced by these invariants is related to the basins of attraction.
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