Rescaling of Markov shifts.
Three results on mixing shapes.
A dynamical interpretation of the global canonical height on an elliptic curve.
Arithmetic and growth of periodic orbits.
The canonical height of an algebraic point on an elliptic curve.
A note on mixing properties of invertible extensions.
Integer sequences and periodic points.
The Abramov-Rokhlin Entropy Addition Formula for Amenable Group Actions.
Automorphisms with exotic orbit growth
The dynamical Mertens' theorem describes asymptotics for the growth in the number of closed orbits in a dynamical system. We construct families of ergodic automorphisms of fixed entropy on compact connected groups with a continuum of growth rates on two different growth scales. This shows in particular that the space of all ergodic algebraic dynamical systems modulo the equivalence of shared orbit-growth asymptotics is not countable. In contrast, for the equivalence relation of measurable isomorphism...
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