Dynamical systems

April 26, 2016 — July 27, 2016

calculus
dynamical systems
geometry
Hilbert space
how do science
Lévy processes
machine learning
neural nets
PDEs
physics
regression
sciml
SDEs
signal processing
statistics
statmech
stochastic processes
sync
time series
uncertainty

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Figure 1

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 Rn. 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 a 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 wizardry”, 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

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