Invariant measures for the Box-Ball System in Z

CHI NGUYEN; LEONARDO ROLLA; PABLO A. FERRARI; MINMIN WANG

Orléans

Seminario; Seminar of Analysis and Dynamical System - MAPMO; 2017

University of Orléans

The box-ball system (BBA) has been introduced by Takahashi and Satsuma in 1990 as a discrete analog of the KdV equation which has many soliton solutions. A carrier with infinitive capacity travels from left to right along boxes located at integers. Each box may contain one ball or be empty. The carrier picks up balls from occupied boxes and leaves carried balls at empty sites. If the initial ball configuration has left density less than 1/2 then the automation is well-defined in $\mathbb{Z}$. The product measure at any density less than 1/2 is invariant. The automaton has many conserved quantities and (non-product) measures. In this work we describe the set of spatially ergodic invariant measures for the BBA. Joint work with Pablo Ferrari, Leonardo Rolla and Minmin Wang.