Diophantine properties of measures invariant with respect to the Gauss map
نویسندگان
چکیده
منابع مشابه
Diophantine Properties of Measures Invariant with Respect to the Gauss Map
Motivated by the work of D. Y. Kleinbock, E. Lindenstrauss, G. A. Margulis, and B. Weiss [7, 8], we explore the Diophantine properties of probability measures invariant under the Gauss map. Specifically, we prove that every such measure which has finite Lyapunov exponent is extremal, i.e. gives zero measure to the set of very well approximable numbers. We show on the other hand that there exist...
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We find the explicit expression of the absolutely continuous invariant measure for the p-numerated generalized Gauss transformation Tp(x) = { p x }. It allows us to generalize a series of results for the canonical continued fractions, such as Khinchin’s constant and Lévy’s constant. 1. The Invariant Measure The Gauss transformation T (x) = { 1 x } has been well studied. It has a strong relation...
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Lifting modules and their various generalizations as some main concepts in module theory have been studied and investigated extensively in recent decades. Some authors tried to present some homological aspects of lifting modules and -supplemented modules. In this work, we shall present a homological approach to -supplemented modules via fully invariant submodules. Lifting modules and H-suppleme...
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ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2014
ISSN: 0021-7670,1565-8538
DOI: 10.1007/s11854-014-0009-8