Ergodicity for p-adic continued fraction algorithms

2020/09/23 by Hui Rao, Rao, Hui, Shin-ichi Yasutomi +1
Mathematics · Computer Science · #advanced mathematical theories #Mathematical Dynamics and Fractals #Chaos-based Image/Signal Encryption

paper · pdf · doi:10.48550/arxiv.2009.11041

Abstract

Following Schweiger's generalization of multidimensional continued fraction algorithms, we consider a very large family of p-adic multidimensional continued fraction algorithms, which include Schneider's algorithm, Ruban's algorithms, and the p-adic Jacobi-Perron algorithm as special cases. The main result is to show that all the transformations in the family are ergodic with respect to the Haar measure.

Related

• Multidimensional p-adic continued fraction algorithms
• On p-adic Multidimensional Continued Fractions
• On the finiteness and periodicity of the p--adic Jacobi--Perron algorithm
• Classical homogeneous multidimensional continued fraction algorithms are ergodic
• Rational approximations, multidimensional continued fractions and lattice reduction