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Since the discovery of Camassa-Holm equation, because of the special properties that peakon gets, it has received considerable attention in modern Mathematics and Physics. Many new integrable dynamic ...
In this talk, we address on the strong rigidity properties from joint integrability in the setting of Anosov diffeomorphisms on tori. More specifically, for an irreducible Anosov diffeomorphism with s...
In recent years there has been a growing interest towards the integrability of systems which, though not Hamiltonian, retain some link to—or common origin with—Hamiltonian systems. One such field is t...
The workshop 揘ew Trends in Low-Dimensional Physics: Quantum Integrability and Applications?focuses on integrability, as one of the most significant concepts of modern science, characterized by a wide ...
The problem of scattering of particles on the line with repulsive interactions, gives rise to some well-known integrable Hamiltonian systems, for example, the nonperiodic Toda lattice or Calogero's sy...
It is known that, if a point in $R^n$ is driven by a bounded below potential $V$, whose gradient is always in a closed convex cone which contains no lines, then the velocity has a finite limit as time...
We define higher pentagram maps on polygons in $P^d$ for any dimension $d$, which extend R.Schwartz's definition of the 2D pentagram map. We prove their integrability for both closed and twisted polyg...
The complete integrability of a generalized Riemann type hydrodynamic system is studied by means of symplectic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, ...
Abstract: The pentagram map is a discrete dynamical system defined on the moduli space of polygons in the projective plane. This map has recently attracted a considerable interest, mostly because its ...
Abstract: We show that SU(2)_L Yangian and q-deformed SU(2)_R symmetries are realized in a two-dimensional sigma model defined on a three-dimensional squashed sphere. These symmetries enable us to dev...
Abstract: The aim of this article is to find all weight modules of degree 1 of a simple complex Lie algebra that integrate to a continuous representation of a simply-connected real Lie group on some H...
Integrability vs Supersymmetry: Poisson Structures of The Pohlmeyer Reduction.
The pentagram map was introduced by R. Schwartz in 1992 for convex planar polygons. Recently, V. Ovsienko, R. Schwartz, and S. Tabachnikov proved Liouville integrability of the pentagram map for gener...
Abstract: The pentagram map was introduced by R. Schwartz in 1992 for convex planar polygons. Recently, V. Ovsienko, R. Schwartz, and S. Tabachnikov proved Liouville integrability of the pentagram map...

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