Dimension of countable intersections of some sets arising in expansions in non-integer bases

• Autorzy: David Färm , Tomas Persson , Jörg Schmeling
• Języki publikacji: EN

Abstrakty

EN

We consider expansions of real numbers in non-integer bases. These expansions are generated by β-shifts. We prove that some sets arising in metric number theory have the countable intersection property. This allows us to consider sets of reals that have common properties in a countable number of different (non-integer) bases. Some of the results are new even for integer bases.

Kategorie tematyczne

• 37C45: Dimension theory of dynamical systems
• 11J83: Metric theory
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 209
• Numer: 2
• Strony: 157-176

Daty

wydano

2010

Twórcy

autor

David Färm

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland
• Centre for Mathematical Sciences, Lund University, Box 118, SE-22100 Lund, Sweden

autor

Tomas Persson

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland

autor

Jörg Schmeling

• Centre for Mathematical Sciences, Lund University, Box 118, SE-22100 Lund, Sweden

Identyfikatory

DOI

10.4064/fm209-2-4