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Mathematics > Dynamical Systems

Title: A Family of Minimal and Renormalizable Rectangle Exchange Maps

Abstract: A domain exchange map (DEM) is a dynamical system defined on a smooth Jordan domain which is a piecewise translation. We explain how to use cut-and-project sets to construct minimal DEMs. Specializing to the case in which the domain is a square and the cut-and-project set is associated to a Galois lattice, we construct an infinite family of DEMs in which each map is associated to a PV number. We develop a renormalization scheme for these DEMs. Certain DEMs in the family can be composed to create multistage, renormalizable DEMs.
Comments: 33 pages, 12 figures
Subjects: Dynamical Systems (math.DS)
Cite as: arXiv:1803.06369 [math.DS]
  (or arXiv:1803.06369v1 [math.DS] for this version)

Submission history

From: Ian Alevy [view email]
[v1] Fri, 16 Mar 2018 18:42:57 GMT (726kb,D)