Related papers: Mertens' theorem for toral automorphisms
It is well-known that the Artin-Mazur dynamical zeta function of a hyperbolic or quasi-hyperbolic toral automorphism is a rational function, which can be calculated in terms of the eigenvalues of the corresponding integer matrix. We give an…
Dynamically stable periodic rotations of a driven pendulum provide a unique mechanism for generating a uniform rotation from bounded excitations. This paper studies the effects of a small ellipticity of the driving, perturbing the classical…
We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are $S_\infty$-invariant and concentrated on a single…
In this article we generalize a theorem of Benson for generalized quadrangles to strongly regular graphs and directed strongly regular graphs. The main result provides numerical restrictions on the number of fixed vertices and the number of…
Transverse parton momentum dependent distribution functions (TMDs) of the nucleon are studied in a covariant model, which describes the intrinsic motion of partons in terms of a covariant momentum distribution. The consistency of the…
Let $M$ be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian $H:T^*M\rightarrow \mathbb R$ and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits…
In this paper we study the properties of the periodic orbits of \"x + V'_x(t, x) = 0 with x \in S1 and V(t, x) a T0 periodic potential. Called {\rho} \in (1/T0)Q the frequency of windings of an orbit in S1 we show that exists an infinite…
The motion of test particles along circular orbits in the vacuum $C$ metric is studied in the Frenet-Serret formalism. Special orbits and corresponding intrinsically defined geometrically relevant properties are selectively studied.
We prove an algebraic extension theorem for the computably enumerable sets, $\mathcal{E}$. Using this extension theorem and other work we then show if $A$ and $\hat{A}$ are automorphic via $\Psi$ then they are automorphic via $\Lambda$…
Unimodular gravity is a modified theory with respect to general relativity by an extra condition that the determinant of the metric is fixed. Especially, if the energy-momentum tensor is not imposed to be conserved separately, a new…
We prove results towards the equidistribution of certain families of periodic torus orbits on homogeneous spaces, with particular focus on the case of the diagonal torus acting on quotients of $\PGL_n(\R)$. After attaching to each periodic…
Different types of nonstandard homology groups based on the various subcomplexes of differential forms are considered as a continuation of the recent authors works. Some of them reflect interesting properties of dynamical systems on the…
Let $R$ be a commutative Noetherian local ring. We study tensor products involving a finitely generated $R$-module $M$ through the natural action of its endomorphism ring. In particular, we study torsion properties of self tensor products…
Consider a topological dynamical system where the group is abelian and the topologies are locally compact and second-countable. Given an invariant measure for this system, we show that if its dynamical spectrum is contained in some Borel…
This is a survey on Valiron's Theorem about the convergence properties of orbits of analytic self-maps of the disk of hyperbolic type and related questions in one and several variables.
Self-dual abelian Higgs system, involving both the Maxwell and Chern-Simons terms are obtained from Carroll-Field-Jackiw theory by dimensional reduction. Bogomol'nyi-type equations are studied from theoretical and numerical point of view.…
We introduce the concept of shape partition of a tensor and formulate a general tensor eigenvalue problem that includes all previously studied eigenvalue problems as special cases. We formulate irreducibility and symmetry properties of a…
We derive the moduli dependent threshold corrections to gauge couplings in toroidal orbifold compactifications. The underlying six dimensional torus lattice of the heterotic string theory is not assumed ---as in previous calculations--- to…
This article reviews a generous sampling of both classical and more recent results on the interplay between measurable and topological dynamics. In the first part we have surveyed the strong analogies between ergodic theory and topological…
Recent experimental observation of inertial spin dynamics calls upon holistic reevaluation of the theoretical framework of magnetic resonance in ferromagnets. Here, we derive the secular equation of an inertial spin system in analogy to the…