Some applications of the individual ergodic theorem to problems in number theory

We show some theorems on strong or uniform strong ergodicity on a nonempty subset of state space at time 0 or at all times, some theorems on weak or strong ergodicity, and a theorem

Automata and formal languages, logic in computer science, compu- tational complexity, infinite words, ω -languages, 1-counter automaton, 2-tape automaton, cardinality problems,

We say that the measure-preserving dynamical system T is 2-fold simple if it has no other ergodic 2-fold self-joinings than the product measure {µ⊗µ} and joinings supported on the

More worryingly, in ergodic theory, the notion of conditionally weakly mixing systems is well- established (see e.g. [13]), but if one where to conceive a notion of conditional

Then the multiple ergodic averages (4.1) converge strongly (weakly) if and only if the entangled averages (4.2) converge in the strong (weak) operator topology.... As was shown in

4.. This completes the construction. Notice that we have not shown that S is uniquely ergodic. In fact there are minimal non uniquely ergodic homeomorphisms of a

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working on algebraic varieties usual Diophantine geometry setup Arakelov geometry defines the height of subvarieties (Faltings, Bost-Gillet-Soulé).. putting all places on equal