Metric properties of N-continued fractions
Dan Lascu
TL;DR
This paper investigates the metric properties of N-continued fractions, exploring the invariant measure and Perron-Frobenius operator associated with the transformation that generates this generalized continued fraction expansion.
Contribution
It provides a detailed analysis of the metric properties, invariant measure, and Perron-Frobenius operator for N-continued fractions, extending previous work on regular continued fractions.
Findings
Derived the invariant measure for the N-continued fraction transformation
Analyzed the Perron-Frobenius operator associated with the expansion
Established metric properties of the N-continued fractions
Abstract
A generalization of the regular continued fractions was given by Burger et al. in 2008 [3]. In this paper we give metric properties of this expansion. For the transformation which generates this expansion, its invariant measure and Perron-Frobenius operator are investigated.
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Taxonomy
TopicsMathematical Dynamics and Fractals · semigroups and automata theory · Computability, Logic, AI Algorithms