# Dynamical systems

April 26, 2016 — July 27, 2016

Remember linear time invariant systems, as made famous by signal processing? Now relax the assumption that the model is linear, or even that its state space is in \(\mathbb{R}^n\). Maybe its state is a measure, or a symbol, or whatever. Now say the word “chaos!”. Pronounce the exclamation mark. Maybe it’s a random system, a stochastic process, or a deterministic process representing the evolution of the measure of stochastic process or whatever.

(Regarding that, one day I should try to understand how Talagrand uses isoperimetric inequalities to derive concentration inequalities.)

Topics that I should connect to this one: the weird end: “nonlinear time series wizardy”, Also “sync”. And “ergodic theory”.

To wish I understood: Takens embedding, and whether it is any statistical use at all.

There is too much to do here, and it’s done better elsewhere. therefore: Idiosyncratic notes only.

## 1 References

*Dynamics–the geometry of behavior*.

*Theory in Biosciences*.

*Neural Networks*.

*Complexity: Hierarchical Structures and Scaling in Physics*. Cambridge Nonlinear Science Series.

*Hidden Markov Models and Dynamical Systems*.

*International Journal of Bifurcation and Chaos*.

*arXiv:1505.05310 [Cs, Stat]*.

*arXiv:1411.5172 [Cs, Stat]*.

*Proceedings of the National Academy of Sciences*.

*Nonlinear Time Series Analysis*.

*Dynamic Patterns: The Self-Organization of Brain and Behavior (Complex Adaptive Systems)*.

*Ecological Monographs*.

*The European Physical Journal Special Topics*.

*Distill*.

*Physical Review Letters*.

*2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)*.

*IEEE Transactions on Information Theory*.

*Brain and Cognition*.

*Physical Review E*.

*Nonlinear Dynamics and Statistics*.

*Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity)*.

*Journal of Ornithology*.

*EPL (Europhysics Letters)*.