Related papers: Remling's Theorem on canonical systems

We establish a sharp upper estimate for the order of a canonical system in terms of the Hamiltonian. This upper estimate becomes an equality in the case of Krein strings. As an application we prove a conjecture of Valent about the order of…

In this paper, we introduce a new canonical connection on Riemannian manifold with a distribution. Moreover, as an application of the connection, we give a geometric proof of the Frobenius theorem.

It is demonstrated that the canonical distribution for a subsystem of a closed system follows directly from the solution of the time-reversible Newtonian equation of motion in which the total energy is strictly conserved. It is shown that…

The Hamilton-Jacobi formalism for fermionic systems is studied. We derive the HJ equations from the canonical transformation procedure, taking into account the second class constraints typical of these systems. It is shown that these…

We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…

We show that every structurally submodular separation system admits a canonical tree set which distinguishes its tangles.

We solve direct and inverse problems for two-dimensional (quasi) canonical systems related to exponential polynomials of a specific but sufficiently general type. The approach to the inverse problem in this paper provides an interpretation…

The aim of this paper is to show that, in the limit circle case, the defect index of a symmetric relation induced by canonical systems, is constant on C. This provides an alternative proof of the De Branges theorem that the canonical…

We investigate two methods of constructing a solution of the Schr\"{o}dinger equation from the canonical transformation in classical mechanics. One method shows that we can formulate the solution of the Schr\"{o}dinger equation from linear…

In this paper we prove the Zariski-Lipman conjecture for log canonical spaces.

The classical Poincar\'e formula relates the rational homology classes of tautological cycles on a Jacobian to powers of the class of Riemann theta divisor. We prove a tropical analogue of this formula. Along the way, we prove several…

We prove general Cramer type theorems for linear systems over various extensions of the tropical semiring, in which tropical numbers are enriched with an information of multiplicity, sign, or argument. We obtain existence or uniqueness…

In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear…

In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.

Dynamical canonical systems and their connections with the classical (spectral) canonical systems are considered. We construct B\"acklund-Darboux transformation and explicit solutions of the dynamical canonical systems. We study also those…

We prove an infinite-dimensional KAM theorem for a Hamiltonian system with sublinear growth frequencies at infinity. As an application, we prove the reducibility of the linear fractional Schr\"odinger equation with quasi-periodic…

We use a classical result of Gollinski and Ibragimov to prove an analog of the strong Szego theorem for Jacobi matrices on $l^2(\N)$. In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences…

We state two recent results concerning the linearization of integrable systems on generalised Jacobians. Then we apply this to the (complexified) spherical pendulum.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

We prove two theorems on the locally finite decompositions of the cones of divisors by the cones which correspond to canonical and minimal models. We introduce the concept of the numerical linear systems in order to simplify the argument on…