A placeholder.

Informally, I am admitting as βstableβ any dynamical system which does not explode super-polynomially fast; We can think of these as systems where if the system is not stationary then at least the rate of change might be.

Here I would like to think how to parameterize stable systems, and how to discover if systems are stable. This in a general context, which can be extremely hard in interesting systems. But often stability questions can be simpler in the context of linear systems, where is is about polynomial root-finding (perversely, polynomial root-finding is itself a famously chaotic system).

In a general setting should probably look at stuff like Lyapunov exponents to quantify stability.

Interesting connections here β we can also think about the relationships between stability and ergodicity, and criticality. Considering stability of neural networks turns out to produce some nice ideas.

## References

*2015 European Control Conference (ECC)*, 2496β2501. Linz, Austria: IEEE.

*arXiv:1709.03698 [Cs, Stat]*.

*Advances in Neural Information Processing Systems*, 34:572β85. Curran Associates, Inc.

*Nonlinear Dynamical Systems and Control: a Lyapunov-Based Approach.*Princeton: Princeton University Press.

*Advances in Neural Information Processing Systems*. Vol. 33.

*The Annals of Probability*25 (3): 1210β40.

*Chaos: An Interdisciplinary Journal of Nonlinear Science*27 (12): 121102.

*arXiv:2106.10165 [Hep-Th, Stat]*, August.

*Nonlinear Dynamics and Statistics*.

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