Talk:Markov odometer

Conservative transformation red link

This article has 'conservative' piped to the red link conservative transformation. It appears that the phrase 'conservative transformation' occurs in ergodic theory. So does the term nonsingular transformation. See this ergodic paper by Danilenko and Silva on the web that might point to how to do this. EdJohnston (talk) 15:49, 27 August 2018 (UTC)[reply]

A system is conservative iff it does not have any wandering set. "Clearly", states the PDF: I quote paragraph 2.2: "Clearly, if T has a wandering set of positive measure then it cannot be conservative." Both conservative transformation and nonsingular transformation should be redirects to conservative system. 67.198.37.16 (talk) 20:25, 11 September 2020 (UTC)[reply]

Ornstein odometer

I'm not sure if "Ornstein odometer" is in common use, but I think Ornstein should be credited as being the first to historically demonstrate a type III ergodic system, and it takes the form of an odometer. At least, that is what I understand the above-cited PDF to be saying. I think this is quite interesting ... no clue if it is an example of a Markov odometer, since that section depends on the definition of the Bratteli–Vershik diagram, which, in it's current form, is a garbled mess. 67.198.37.16 (talk) 06:13, 12 September 2020 (UTC)[reply]

Started. Todo: explain type III apparently there aren't any WP articles that do this. A discussion of the spectrum of odometers is also needed. This article should probably be split in two: odometer (dynamical systems) for the first part, and Markov odometer for the main topic. 67.198.37.16 (talk) 15:30, 19 September 2020 (UTC)[reply]

Split into multiple articles

This article needs to be split into multiple articles; my edits have been morphing this article away from being about markov odometers to being about odometers in general. 67.198.37.16 (talk) 19:01, 21 October 2020 (UTC)[reply]