Related papers: Hamiltonians arising from L-functions in the Selbe…

The Deligne-Simpson problem is formulated like this: give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\subset SL(n,{\bf C})$ or $c_j\subset sl(n,{\bf C})$ so that there exist irreducible $(p+1)$-tuples of…

Working with a general class of linear Hamiltonian systems with at least one singular boundary condition, we show that renormalized oscillation results can be obtained in a natural way through consideration of the Maslov index associated…

The Hamiltonian formulation for the mechanical systems with reparametrization-invariant Lagrangians, depending on the worldline external curvatures is given, which is based on the use of moving frame. A complete sets of constraints are…

We formulate a generalization of Riesz-type criteria in the setting of $L$-functions belonging to the Selberg class. We obtain a criterion which is sufficient for the Grand Riemann Hypothesis (GRH) for $L$-functions satisfying axioms of the…

We construct a Hamiltonian formulation for the class of plane-fronted gravitational waves with parallel rays (pp-waves). Because of the existence of a light-like Killing vector, the dynamics is effectively reduced to a 2+1 evolution with…

A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a…

The Hamiltonian treatment of constrained systems in $G\ddot{u}ler's$ formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a…

In this paper new classes of $L_2$-orthogonal functions are constructed as iterated $L_2$-orthogonal systems. In order to do this we use the theory of the Riemann's zeta-function as well as our theory of Jacob's ladders. The main result is…

A basic problem in smooth dynamics is determining if a system can be distinguished from its inverse, i.e., whether a smooth diffeomorphism $T$ is isomorphic to $T^{-1}$. We show that this problem is sufficiently general that asking it for…

Assuming the Generalized Riemann Hypothesis, we provide uniform upper bounds with explicit main terms for moduli of $\left(\cL'/\cL\right)(s)$ and $\log{\cL(s)}$ for $1/2+\delta\leq\sigma<1$, fixed $\delta\in(0,1/2)$ and for functions in…

We develop a constructive procedure for arriving at the Hamilton-Jacobi framework for the so-called affine in acceleration theories by analysing the canonical constraint structure. We find two scenarios in dependence of the order of the…

We present a definition of generating functions of canonical relations, which are real functions on symmetric symplectic spaces, discussing some conditions for the presence of caustics. We show how the actions compose by a neat geometrical…

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…

We discuss a general and systematic method for obtaining effective Hamiltonians that describe different nonlinear optical processes. The method exploits the existence of a nonlinear deformation of the usual su(2) algebra that arises as the…

The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and…

There have been a number of recent works on the theory of period polynomials and their zeros. In particular, zeros of period polynomials have been shown to satisfy a "Riemann Hypothesis" in both classical settings and for cohomological…

The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdetermination of the commutator or Poisson bracket relations. The…

We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…

Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…

We study the eigenfunctions of the classical Liouville operator and investigate the conditions they must obey to be separable as a product state. We point out that the conditions for separability are equivalent to requirements of…