Matching for a family of infinite measure continued fraction transformations
| Autor: | Sara Munday, Niels Langeveld, Charlene Kalle, Marta Maggioni |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
Sigma Dynamical Systems (math.DS) Parameter space Absolute continuity Fixed point Lebesgue integration Combinatorics symbols.namesake 11K50 37A05 37A35 37A40 11A55 28D05 37E05 Hausdorff dimension symbols FOS: Mathematics Discrete Mathematics and Combinatorics Entropy (information theory) Invariant measure Mathematics - Dynamical Systems Analysis Mathematics |
| Popis: | As a natural counterpart to Nakada's $\alpha$-continued fraction maps, we study a one-parameter family of continued fraction transformations with an indifferent fixed point. We prove that matching holds for Lebesgue almost every parameter in this family and that the exceptional set has Hausdorff dimension 1. Due to this matching property, we can construct a planar version of the natural extension for a large part of the parameter space. We use this to obtain an explicit expression for the density of the unique infinite $\sigma$-finite absolutely continuous invariant measure and to compute the Krengel entropy, return sequence and wandering rate of the corresponding maps. Comment: 17 pages, 5 figures |
| Databáze: | OpenAIRE |
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