Lund, 22nd - 24th January 2004
Quantum Ergodicity - Basic Ideas and Recent Developments
Ergodicity in p-adic dynamics
Karl-Olof Lindahl (Växjö)
We give necessary and sufficient conditions for
ergodicity of dynamics generated by p-adic power series. In 
it was shown that a p-adic monomial map of the form f(x)=xn
is minimal on all spheres of radius less than 1, centered at
x=1, if and only if n is a generator of the group of units
modulo p2. Moreover, in this case (in fact for all isometries
on compact open subsets of the p-adic numbers as shown in
the properties of minimality, ergodicity, and unique ergodicity
are equivalent. These results were taken a bit further in , for
some special type of polynomials. We show that these results are
true also for a general power series near a fixed point .
 M. Gundlach, A. Khrennikov, and K.-O. Lindahl. On ergodic
behavior of p-adic dynamical systems. Inf. Dimens. Anal.
Prob. Relat. Top., 4(4):569-577, 2001.
 J. Bryk, C.E. Silva. p-adic measurable dynamical systems of
simple polynomials. Amer. Math. Monthly, accepted.
 K.-O. Lindahl. On conjugation, ergodicity and minimality of
p-adic holomorphic functions. Preprint, 2003.
Last modified: Jan 28 2004