Mathematics – Dynamical Systems
Scientific paper
2011-05-25
Mathematics
Dynamical Systems
Scientific paper
We generalize the proof of Karamata's Theorem by the method of approximation by polynomials to the operator case. As a consequence, we offer a simple proof of \emph{uniform dual ergodicity} for a very large class of dynamical systems with infinite measure, and we obtain bounds on the convergence rate. In many cases of interest, including the Pomeau-Manneville family of intermittency maps, the estimates obtained through real Tauberian remainder theory are very weak. Building on the techniques of complex Tauberian remainder theory, we develop a method that provides \emph{second (and higher) order asymptotics}. In the process, we derive a \emph{higher order Tauberian theorem} for scalar power series, which to our knowledge, has not previously been covered.
Melbourne Ian
Terhesiu Dalia
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