Automata in groups and dynamics and induced systems of PDE in tropical geometry
Author:
- Tsuyoshi KatoTKTsuyoshi Kato
Preprint
Abstract
In this paper we develop a dynamical scaling limit from rational dynamics to automata in tropical geometry. We compare these dynamics and induce uniform estimates of their orbits. We apply these estimates to introduce a comparison analysis of theory of automata groups in geometric group theory with analysis of rational dynamics and some PDE systems. Frameworks of characteristic properties of automata groups are inherited to the corresponding rational or PDE dynamics. As an application we study the Burnside problem in group theory and translate the property as the infinite quasi-recursiveness in rational dynamics.Keywords
All Related Versions
This publication has 11 references indexed in Scilit:
- An Asymptotic Comparison of Differentiable Dynamics and Tropical GeometryMathematical Physics, Analysis and Geometry, 2011
- On amenability of automata groupsDuke Mathematical Journal, 2010
- Deformations of Real Rational Dynamics in Tropical GeometryGeometric and Functional Analysis, 2009
- On exponential growth and uniformly exponential growth for groupsInventiones Mathematicae, 2004
- The Lamplighter Group as a Group Generated by a 2-state Automaton, and its SpectrumGeometriae Dedicata, 2001
- The correspondence principle for idempotent calculus and some computer applications1998
- From Soliton Equations to Integrable Cellular Automata through a Limiting ProcedurePhysical Review Letters, 1996
- Conserved Quantities of a Class of Nonlinear Difference-Difference EquationsJournal of the Physical Society of Japan, 1995
- Discriminants, Resultants, and Multidimensional Determinants1994
- Integrable mappings and soliton equations IIPhysica D: Nonlinear Phenomena, 1989