Number theory and dynamical systems on foliated spaces

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.

References in corpus (1)

• Real polarizable Hodge structures arising from foliations

Cited by in corpus (13)

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• On $3$-dimensional foliated dynamical systems and Hilbert type reciprocity law
• A remark on a relation between foliations and number theory
• Non-commutative geometry, dynamics, and infinity-adic Arakelov geometry
• A Coincidence Formula for Foliated Manifolds
• On the analogy between L-functions and Atiyah-Bott-Lefschetz trace formulas for foliated spaces
• Noncommutative Geometry in the Framework of Differential Graded Categories
• Scaling group flow and Lefschetz trace formula for laminated spaces with $p-$adic transversal
• Abelian varieties and transversal index theorems
• Leafwise cohomological expression of dynamical zeta functions on foliated dynamical systems