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Rotation sets for subshifts of finite type. (English) Zbl 0821.58017
The paper introduces notions of the rotation set, the rotation vector of a dynamical system \((X,f)\) and a function \(\varphi : X \to \mathbb{R}^ n\) and explains their role. The main result states that when \((X,f)\) is a transitive subshift of finite type and \(\varphi\) depends only on the cylinders of length 2, then the rotation set is a convex polyhedron (i.e. the convex hull of a finite set), rotation vectors of periodic points form a dense subset of the rotation set and every point of its interior is a rotation vector of an ergodic invariant probability measure.

MSC:
37E99 Low-dimensional dynamical systems
54H20 Topological dynamics (MSC2010)
37A99 Ergodic theory
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