Abelian Networks IV. Dynamics of Nonhalting Networks.

Cover
Title page
Chapter 1. Introduction
1.1. Flashback
1.2. Atemporal dynamics
1.3. Relating atemporal dynamics to traditional dynamics
1.4. Computational questions
1.5. The torsion group of a nonhalting abelian network
1.6. Critical networks
1.7. Example: Rotor networks and abelian mobile agents
1.8. Proof ideas
1.9. Summary of notation
Chapter 2. Commutative Monoid Actions
2.1. Injective actions and Grothendieck group
2.2. The case of finite commutative monoids
Chapter 3. Review of Abelian Networks
3.1. Definition of abelian networks
3.2. Legal and complete executions
3.3. Locally recurrent states
3.4. The production matrix
3.5. Subcritical, critical, and supercritical abelian networks
3.6. Examples: sandpiles, rotor-routing, toppling, etc
Chapter 4. The Torsion Group of an Abelian Network
4.1. The removal lemma
4.2. Recurrent components
4.3. Construction of the torsion group
4.4. Relations to the critical group in the halting case
Chapter 5. Critical Networks: Recurrence
5.1. Recurrent configurations and the burning test
5.2. Thief networks of a critical network
5.3. The capacity and the level of a configuration
5.4. Stoppable levels: When does the torsion group act transitively?
Chapter 6. Critical Networks: Dynamics
6.1. Activity as a component invariant
6.2. Near uniqueness of legal executions
Chapter 7. Rotor and Agent Networks
7.1. The cycle test for recurrence
7.2. Counting recurrent components
7.3. Determinantal generating functions for recurrent configurations
Chapter 8. Concluding Remarks
8.1. A unified notion of recurrence and burning test
8.2. Forbidden subconfiguration test for recurrence
8.3. Number of recurrent configurations in a recurrent component
Acknowledgement
Bibliography
Back Cover.