Marchenko-Ostrovski mappings for periodic Jacobi matrices

We consider the 1D periodic Jacobi matrices. The spectrum of this operator is purely absolutely continuous and consists of intervals separated by gaps. We solve the inverse problem (including characterization) in terms of vertical slits on the quasimomentum domain . Furthermore, we obtain a priori two-sided estimates for vertical slits in terms of Jacoby matrices

Periodic Jacobi operator with finitely supported perturbation on the half-lattice

We consider the periodic Jacobi operator $J$ with finitely supported perturbations on the half-lattice. We describe all eigenvalues and resonances of $J$ and give their properties. We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the Jost functions is one-to-one and onto, we show how the Jost functions can be reconstructed from the eigenvalues, resonances and the set of zeros of S(\l)-1, where S(\l) is the scattering matrix.Comment: 29 page

Tame majorant analyticity for the Birkhoff map of the defocusing nonlinear Schr\uf6dinger equation on the circle

For the defocusing nonlinear Schr\uf6 dinger equation on the circle, we construct a Birkhoff map \u3a6 which is tame majorant analytic in a neighborhood of the origin. Roughly speaking, majorant analytic means that replacing the coefficients of the Taylor expansion of \u3a6 by their absolute values gives rise to a series (the majorant map) which is uniformly and absolutely convergent, at least in a small neighborhood. Tame majorant analytic means that the majorant map of \u3a6 fulfills tame estimates. The proof is based on a new tame version of the Kuksin-Perelman theorem (2010 Discrete Contin. Dyn. Syst. 1 1-24), which is an infinite dimensional Vey type theorem

On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators

The article is devoted to the following question. Consider a periodic self-adjoint difference (differential) operator on a graph (quantum graph) G with a co-compact free action of the integer lattice Z^n. It is known that a local perturbation of the operator might embed an eigenvalue into the continuous spectrum (a feature uncommon for periodic elliptic operators of second order). In all known constructions of such examples, the corresponding eigenfunction is compactly supported. One wonders whether this must always be the case. The paper answers this question affirmatively. What is more surprising, one can estimate that the eigenmode must be localized not far away from the perturbation (in a neighborhood of the perturbation's support, the width of the neighborhood determined by the unperturbed operator only). The validity of this result requires the condition of irreducibility of the Fermi (Floquet) surface of the periodic operator, which is expected to be satisfied for instance for periodic Schroedinger operators.Comment: Submitted for publicatio

Singularities of bi-Hamiltonian systems

We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties of compatible Poisson brackets. As the main tool, we introduce the notion of linearization of a Poisson pencil. From the algebraic viewpoint, a linearized Poisson pencil can be understood as a Lie algebra with a fixed 2-cocycle. In terms of such linearizations, we give a criterion for non-degeneracy of singular points of bi-Hamiltonian systems and describe their types

Global Birkhoff coordinates for the periodic Toda lattice

In this paper we prove that the periodic Toda lattice admits globally defined Birkhoff coordinates.Comment: 32 page

The Self-Selection of Democracies into Treaty Design: Insights from International Environmental Agreements

Generally, democratic regime type is positively associated with participating in international environmental agreements. In this context, this study focuses on the legal nature of an agreement, which is linked to audience costs primarily at the domestic level that occur in case of non-compliance and are felt especially by democracies. Eventually, more legalized (\hard-law") treaties make compliance potentially more challenging and democratic leaders may anticipate the corresponding audience costs, which decreases the likelihood that democracies select themselves into such treaties. The empirical implication of our theory follows that environmental agreements with a larger share of democratic members are less likely to be characterized by hard law. This claim is tested using quantitative data on global environmental treaties. The results strongly support our argument, shed new light on the relationship between participation in international agreements and the form of government, and also have implications for the \words-deeds" debate in international environmental policy-making