相关论文: Number theory and dynamical systems on foliated sp…

We give a relation between Deninger's foliated dynamical systems associated to abelian number fields and Connes-Consani's adelic spaces. It fits with the analogy between knots and primes in arithmetic topology and lights up a geometric view…

This report on the topics in the title was written for a lecture series at the Southwestern Center for Arithmetic Algebraic Geometry at the University of Arizona.It may serve as an introduction to certain conjectural relations between…

We point out analogies between (a) the explicit formulas in analytic number theory and transversal index theory, (b) Lichtenbaum's recent conjectures on special values of Hasse-Weil zeta functions and a formula for special values of Ruelle…

An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…

The paper gives a categorical approach to generalized manifolds such as orbit spaces and leaf spaces of foliations. It is suggested to consider these spaces as sets equipped with some additional structure which generalizes the notion of…

We discuss analogies between the etale site of arithmetic schemes and the algebraic topology of dynamical systems. The emphasis is on Lefschetz numbers. We also discuss similarities between infinite primes in arithmetic and fixed points of…

The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical…

This survey paper is not a complete reference guide to number-theoretical applications of ergodic theory. Instead, it considers an approach to a class of problems involving Diophantine properties of $n$-tuples of real numbers, namely,…

We give a survey of the approaches to classifying foliations, starting with the Haefliger classifying spaces and the various results and examples about the secondary classes of foliations. Various dynamical properties of foliations are…

We interpret a formula for meromorphic functions on foliations by Riemann surfaces as an analogue to the product formula of valuations in algebraic number theory.

The space of couplings of a given theory is the arena of interest in this article. Equipped with a metric ansatz akin to the Fisher information matrix in the space of parameters in statistics (similar metrics in physics are the…

Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…

The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be…

These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…

A generalized scalar-tensor theory is investigated whose cosmological term depends on both a scalar field and its time derivative. A correspondence with solutions of five-dimensional Space-Time-Matter theory is noted. Analytic solutions are…

We express some basic properties of Deninger's conjectural dynamical system in terms of morphisms of topoi. Then we show that the current definition of the Weil-\'etale topos satisfies these properties. In particular, the flow, the closed…

We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific…

This work explores the space of foliations on projective spaces over algebraically closed fields of positive characteristic, with a particular focus on the codimension one case. It describes how the irreducible components of these spaces…

We combine the theory of traces in homotopical algebra with sheaf theory in derived algebraic geometry to deduce general fixed point and character formulas. The formalism of dimension (or Hochschild homology) of a dualizable object in the…

A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…