Arithmetic Dynamics
By Nikita Sidorov. 2002
70 citations recorded by the source corpus.
. This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a “dynamical” sense. This means precisely that they (semi-) conjugate a given continuous (or measure-preserving) dynamical system and a symbolic one. The classes of dynamical systems and their codings considered in the paper involve: We study ergodic-theoretic and probabilistic properties of these expansions and their applications. Besides, in some cases we create “redundant” representations (those whose space of “digits” is a priori larger than necessary) and study their combinatorics.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/28d8ffea42aadecfd1201324b8f306f9cd2f2e96
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In Computational Theory and Mathematics
- Anne Siegel
- Val'erie Berth'e
- Marcy Barge
- Wenxia Li
- Derong Kong
- J.-Y. Lee
- Vilmos Komornik
- Shigeki Akiyama
In Geometry and Topology
In Mathematical Physics
- Anne Siegel
- Val'erie Berth'e
- Marcy Barge
- Wenxia Li
- Derong Kong
- J.-Y. Lee
- Vilmos Komornik
- Shigeki Akiyama
Citations in the corpus
- On the Pisot Substitution Conjecture (2015, background): “In [70] and [106] this construction arises in the general framework of arithmetic dynamics and arithmetic codings.”
- Hausdorff dimension of univoque sets and Devil's staircase (2015, methodology): “We refer to the papers [23], [6], [7], [8], [9], [3] and surveys [32], [20] and [10] for more information.”