Related papers: Mahler's Work and Algebraic Dynamical Systems
We investigate the dynamics of continued fractions and explore the ergodic behaviour of the products of mixed partial quotients in continued fractions of real numbers. For any function $\Phi:\mathbb N\to [2,+\infty)$ and any integer $d\geq…
The standard Hamiltonian machinery, being applied to field theory, leads to infinite-dimensional phase spaces. It is not covariant. In this article, we present covariant finite-dimensional multimomentum Hamiltonian formalism for field…
The paper extends basic Einstein--Hilbert action by adding a newly proposed invariant constructed from a specific contraction between the Einstein tensor and the energy momentum tensor, encoding a non--minimal coupling between the…
In this paper we introduce for a group $G$ the notion of ultralimit of measure class preserving actions of it, and show that its Furstenberg-Poisson boundaries can be obtained as an ultralimit of actions on itself, when equipped with…
The geometric nature of Euler fluids has been clearly identified and extensively studied over the years, culminating with Lagrangian and Hamiltonian descriptions of fluid dynamics where the configuration space is defined as the…
We survey some recent developments and applications of the study of the rigidity properties of natural algebraic actions of multidimensional abelian groups.
The use in the action integral of a volume element of the form $\Phi d^{D}x$ where $\Phi$ is a metric independent measure can give new interesting results in all types of known generally coordinate invariant theories: (1) 4-D theories of…
In 1965 Adler, Konheim and McAndrew defined the topological entropy for continuous self-maps of compact spaces. Topological entropy is very well-understood for endomorphisms of compact Abelian groups. A fundamental result in this context is…
A general framework for investigating topological actions of $Z^d$ on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower-dimensional subspaces of $R^d$. Here we completely describe this expansive…
This paper provides a new approach to proving generalizations of the F.&M. Riesz Theorem, for example, the result of Helson and Lowdenslager, the result of Forelli (and de Leeuw and Glicksberg), and more recent results of Yamagushi. We…
We discuss selected topics of current research interest in the theory of dynamical systems, with emphasis on dimension theory, multifractal analysis, and quantitative recurrence. The topics include the quantitative versus the qualitative…
We study the dynamics of the field equations in a five-dimensional spatially flat Friedmann-Lema\^itre-Robertson-Walker metric in the context of a Gauss-Bonnet-Scalar field theory where the quintessence scalar field is coupled to the…
In this paper we study the emergence of coherence in collective motion described by a system of interacting motiles endowed with an inner, adaptative, steering mechanism. By means of a nonlinear parametric coupling, the system elements are…
Actions of $\mathbb{Z}^d$ by automorphisms of compact zero-dimensional groups exhibit a range of mixing behaviour. Schmidt introduced the notion of mixing shapes for these systems, and proved that non-mixing shapes can only arise…
This study derives geometric, variational discretizations of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central role in these discretizations is played by the geometric…
In 1969, I. Bernstein and S. Gelfand introduced an object, which is now called the zeta Mahler function (ZMF, also zeta Mahler measure) and related to the Mahler measure. Here we discuss a family of ZMFs attached to the Laurent polynomials…
Ergodic theory includes several notions of entropy for probability-preserving actions of countable groups. These include Kolmogorov--Sinai entropy based on F\o lner sequences for amenable groups, entropy defined using a random ordering of…
The coupled equations that describe the effect of large-scale magnetic and velocity fields on forced high-diffusivity magnetohydrodynamic flows are investigated through an extension of mean field electrodynamics. Our results generalise…
Furstenberg--Zimmer structure theory refers to the extension of the dichotomy between the compact and weakly mixing parts of a measure preserving dynamical system and the algebraic and geometric descriptions of such parts to a conditional…
Let $A$ be a finite dimensional algebra over an algebraically closed field $k$. Assume $A$ is a basic connected and triangular algebra with $n$ pairwise non-isomorphic simple modules. We consider the {\em Coxeter transformation} $\phi_A(T)$…