Parallel chip-firing on the complete graph: Devil’s staircase and Poincaré rotation number

DOI10.1017/S0143385710000088zbMath1234.37036arXiv0811.2800MaRDI QIDQ3012886

Lionel Levine

Publication date: 7 July 2011

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.2800

zbMATH Keywords

devil's staircaseparallel chip-firingPoincaré numbershort period attractor

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Rotation numbers and vectors (37E45)

Related Items (3)

Abelian networks IV. Dynamics of nonhalting networks ⋮ An exact bound on the number of chips of parallel chip-firing games that stabilize ⋮ On the limited increment parallel chip-firing game

Cites Work

• Unnamed Item
• Chip-firing games on graphs
• Parallel chip firing games on graphs
• No polynomial bound for the period of the parallel chip firing game on graphs
• Self-organized critical state of sandpile automaton models

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