Ergodic Theory of Fibred Systems and Metric Number Theory

Several questions of metric number theory can be handled by the application of ergodic theory. Such an application is possible if an appropriate dynamical system (fibred system) can be constructed which displays some ergodic properties. In this book the notion of a fibred system is considered.

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Several questions of metric number theory can be successfully handled by the application of ergodic theory. Such an application is possible if an appropriate dynamical system (called fibred system) can be constructed which displays some nice ergodic properties. In this book the basic notion of a fibred system is considered. Most of these systems are connected with f-expansions i.e. generalizations of decimal expansions and continued fractions. There is ample treatment of multidimensional continued fractions including the recent applications of subadditive ergodic theorems to Diophantine approximation. Next, basic properties like ergodicity, conservativity, and existence of invarient measures are discussed. Here several auxiliary constructions as first return map or jim transformation are useful. As a further basic tool the Ruelle-Frobenius-Perron transfer operator is considered.