Ergodicity Of P-adic Jacobi-Perron Transfomation

Let X=[0,1],we define the continued fraction expansions of real numbers with the Gauss map T(x)=1/x(mod1),d?=1/log 1/1+xdx.is the invariant measure and ergodic measure of Gauss map,and we can call that ? is Gauss' measure.p is prime,to define the continued fraction expansions of p-adic field,Schneider define the Schneider transformation ?(x)= pv(x)/x-?(pv(x)/x).Hirsh and Washington has proved that the invariant measure and ergodic measure of Schneider transfor-.mation is uniformly Bernoulli measure which is equivelent to the Lebesgue measure in R.The classical Jacobi-Perron algorithms is defined in multidimensional Euclidean vector space.To difine the continued fraction expansions of pZp,Yasutomi defines the modification of Jacobi-Perron algorithm We have proved that the uniformly Bernoulli measure is the ergodic measure of Jacobi-Perron algorithms.