  We discuss analogies between number theory and the theory of dynamical
systems on spaces with a one-codimensional foliation. The emphasis is on
comparing the "explicit formulas" of analytic number theory with certain
dynamical Lefschetz trace formulas. We also point out a possible relation
between an Arakelov-Euler characteristic and an Euler characteristic in the
sense of Connes. Finally the role of generalized solenoids as phase spaces in
our picture is explained.
