Related papers: Torus Actions and Integrable Systems
The gauge invariant method for calculation of the effective action of the local composite fields in QFT is proposed. The effective action of the local composite fields in QED is studied up to 2-loop level. The graph rules for the local…
Invariant torus are constructed under assumption that the homogeneous system admits an exponential dichotomy on the semi-axes. The main result is closely related with the well-known Palmer's lemma and results of Boichuk A.A., Samoilenko…
We investigate linear parabolic maps on the torus. In a generic case these maps are non-invertible and discontinuous. Although the metric entropy of these systems is equal to zero, their dynamics is non-trivial due to folding of the image…
In these lecture notes, we give an introduction to cluster integrable systems. The topics include relativistic Toda systems, moduli spaces of framed local systems, Goncharov-Kenyon integrable systems, and quantization.
Different group structures which underline the integrable systems are considered. In some cases, the quantization of the integrable system can be provided with substituting groups by their quantum counterparts. However, some other group…
This paper studies system theoretic properties of the class of difference inclusions of convex processes. We will develop a framework considering eigenvalues and eigenvectors, weakly and strongly invariant cones, and a decomposition of…
We prove a Morse index theorem for action functionals on paths that are allowed to reflect at a hypersurface (either in the interior or at the boundary of a manifold). Both fixed and periodic boundary conditions are treated.
By studying completely integrable torus actions on contact manifolds we prove a conjecture of Toth and Zelditch that toric integrable geodesic flows on tori must have flat metrics.
An upper bound is obtained on the rank of a torus which can act smoothly and effectively on a smooth, closed, simply connected, rationally elliptic manifold. In the maximal-rank case, the manifolds admitting such actions are classified up…
In this paper, we classify smooth, contractible affine varieties equipped with faithful torus actions of complexity two, having a unique fixed point and a two-dimensional algebraic quotient isomorphic to a toric blow-up of a toric surface.…
The purpose of this paper is to survey the structure of closed and transitive transformation groups acting on a closed surface. In particular, we prove a number of relations between groups acting on the sphere that contain the rotation…
The reduced system in the Clebsch problem of the motion of a rigid body in fluid treated as the motion of a rigid body about its fixed mass center in a central Newtonian field with zero value of the area integral is a completely integrable…
In this paper we address two questions concerning the effective action of a topological insulator in one and three dimensional space without boundaries, such as a torus. The first is whether a uniform $\theta$-term with $\theta=\pi$ is…
We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville-Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrability and the Mishchenko-Fomenko theorem on noncommutative…
A new ansatz is presented for a Lax pair describing systems of particles on the line interacting via (possibly nonsymmetric) pairwise forces. Particular cases of this yield the known Lax pairs for the Calogero-Moser and Toda systems, as…
We establish a generic sufficient condition for a compact $n$-dimensional manifold bearing an integrable geodesic flow to be the $n$-torus. As a complementary result, we show that in the case of domains of possible motions with boundary,…
Collective actuation in active solids, the spontaneous condensation of the dynamics on a few elastic modes, takes place whenever the deformations of the structure reorient the forces exerted by the active units composing, or embedded in,…
For the n-dimensional integrable system with a twisted so(p,q) reduction, Darboux transformations given by Darboux matrices of degree 2 are constructed explicitly. These Darboux transformations are applied to the local isometric immersion…
In this paper we study general torus actions on manifolds with isolated fixed points from combinatorial point of view. The main object of study is the poset of face submanifolds of such actions. We introduce the notion of a locally…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…