Displaying similar documents to “Universal expansions in negative and complex bases.”

Generalized golden ratios of ternary alphabets

Vilmos Komornik, Anna Chiara Lai, Marco Pedicini (2011)

Journal of the European Mathematical Society

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Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases...

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

David Färm, Tomas Persson, Jörg Schmeling (2010)

Fundamenta Mathematicae

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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.

M-bases in spaces of continuous functions on ordinals

Ondrej F. K. Kalenda (2002)

Colloquium Mathematicae

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We prove, among other things, that the space C[0,ω₂] has no countably norming Markushevich basis. This answers a question asked by G. Alexandrov and A. Plichko.