SHRINKING TARGETS FOR NONAUTONOMOUS DYNAMICAL SYSTEMS CORRESPONDING TO CANTOR SERIES EXPANSIONS

Autor:	Bill Mance, Mariusz Urbański, David Simmons, Lior Fishman
Rok vydání:	2015
Předmět:	Discrete mathematics Dynamical systems theory General Mathematics Hausdorff dimension Interval (mathematics) Diophantine approximation Type (model theory) Dynamical system (definition) Series expansion Mathematics Interpretation (model theory)
Zdroj:	Bulletin of the Australian Mathematical Society. 92:205-213
ISSN:	1755-1633 0004-9727
DOI:	10.1017/s0004972715000441
Popis:	We provide a closed formula of Bowen type for the Hausdorff dimension of a very general shrinking target scheme generated by the nonautonomous dynamical system on the interval$[0,1)$, viewed as$\mathbb{R}/\mathbb{Z}$, corresponding to a given method of Cantor series expansion. We also examine a wide class of examples utilising our theorem. In particular, we give a Diophantine approximation interpretation of our scheme.
Databáze:	OpenAIRE
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