Talk:Markov partition

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Low	This article has been rated as Low-priority on the project's priority scale.

Systems Mid‑importance

	Systems science portal This article is within the scope of WikiProject Systems, which collaborates on articles related to systems and systems science.SystemsWikipedia:WikiProject SystemsTemplate:WikiProject SystemsSystems articles
Mid	This article has been rated as Mid-importance on the project's importance scale.
	This article is within the field of Dynamical systems.

This really isn't all that complicated[edit]

The idea of a Markov partition is, conceptually, quite simple. Consider an iterated linear map of the unit square into itself. (This can be represented by a 2x2 matrix, with translation of a transformed point back into the unit square – think of co-ordinates computed modulo 1.) In general, such a map will have eigenvectors, which represent two lines that get translated into themselves by the iterated mapping. Shifted back inside the unit square, these lines produce the "Markov partition" – the lines divide the square into regions which "mix" with themselves as the mapping is iterated, but points in one region cannot migrate across the boundary lines defined by the eigenvectors to "mix" with another region.

I found a fairly good description of this phenomenon at this web site.

I'll try to write a more elementary description for the article. A picture could be very helpful here. Unfortunately, I don't have much facility with drawing pictures. Can someone else help? DavidCBryant 15:49, 24 July 2007 (UTC)[reply]