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Renormalization on the \(n\)-dimensional torus. (English) Zbl 0761.58008
A renormalization group theory at the topological level is presented for a large class of maps on the \(n\)-dimensional torus \(T^ n\). This class includes all maps which are topologically conjugate to a rotation on \(T^ n\).
The key concept is the notion of “even \(n\)-colourings of the integers”. A natural way to code rotations on \(T^ n\) in which the coding domains are renormalization regions is described. It is based on the generalization of the relation to kneading theory which exists in dimension one. Then, the construction is extended to maps of the torus which are topologically conjugate to a rotation. It is pointed out that some results valid for rotations become false for a particular class of maps (called Denjoy maps).
Reviewer: G.Zet (Iaşi)

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37A99 Ergodic theory
54H20 Topological dynamics (MSC2010)
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