English

Number theory and dynamical systems on foliated spaces

Number Theory 2007-05-23 v1 Differential Geometry Dynamical Systems

Abstract

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.

Keywords

Cite

@article{arxiv.math/0204110,
  title  = {Number theory and dynamical systems on foliated spaces},
  author = {Christopher Deninger},
  journal= {arXiv preprint arXiv:math/0204110},
  year   = {2007}
}