Representing a Markov chain as an iterated function system.

For univariate rational functions, boundedness implies Lipschitz continuity. But what happens in the multivariate setting?

I am fascinated by fixed point theory, which (in the constructive case)^[Unlike the famously non-constructive Brouwer fixed point theorem, which only claims existence of a fixed point.] often is based on function iteration until a limit is reached. The simplicity but also power of this hides behind many mathematical subjects, from recursion theory (doh!) to dynamical systems, or even advanced numerical algorithms. Recently, while working on a proof and motivated by examples like fractional derivates, I wondered if we can generalize this function iteration.

A personal note.

Since there is advent of code..

Inheritance sometimes fails to capture the real world. A particular encounter is with linear and affine expressions, as explained in this post.

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