On the Metrical Theory of a Generalized Continued Fraction Expansion
Dan Lascu, Katsunori Kawamura
TL;DR
This paper develops a metrical theory for a new class of generalized continued fraction expansions, deriving probability formulas and establishing the existence of invariant measures for the associated transformations.
Contribution
It introduces a novel continued fraction expansion, provides probability formulas for incomplete quotients, and proves the existence of invariant measures for the related transformations.
Findings
Probability formulas for incomplete quotients
Existence of invariant measures
New class of continued fraction expansions
Abstract
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the continued fraction transformations associated with expansions.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematical and Theoretical Analysis · Functional Equations Stability Results