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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Integrability and constructions of the peakon systems
peakon系统 可积性 构造 Camassa-Holm方程
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2023/11/13
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 ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Spectral rigidity and joint integrability for Anosov diffeomorphisms on tori
环形 阿诺索夫微分同胚 谱刚度 联合可积性
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2023/4/14
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stokes phenomenon and isomonodromy deformation equations: Explicit solution to the Riemann-Hilbert problem and integrability of the isomonodromy equation
斯托克斯现象 等单向变形方程 黎曼-希尔伯特问题 显式解 单场方程 可积性
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2023/5/6
Stokes phenomenon states that the asymptotic behavior of functions can differ in different regions of the complex plane, and that these differences can be described in a quantitative way. These quanti...
Workshop on Dynamics and integrability of nonholonomic and other non-Hamiltonian systems
Workshop Dynamics and integrability of nonholonomic and other non-Hamiltonian systems
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2017/12/20
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...
Liouville-Arnold integrability for scattering under cone potentials
Liouville-Arnold integrability scattering cone potentials Dynamical Systems
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2012/4/26
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...
Complete Integrability for Hamiltonian Systems with a Cone Potential
Complete Integrability Hamiltonian Systems Cone Potential
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2012/4/26
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...
Integrability of higher pentagram maps
Integrability of higher pentagram maps Dynamical Systems
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2012/4/23
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...
Liouville-Arnold integrability of the pentagram map on closed polygons
Liouville-Arnold integrability closed polygons Dynamical Systems
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2011/9/14
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 ...
Integrability of weight modules of degree 1
Integrability of weight modules Representation Theory Hilbert space
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2011/8/26
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 of the Pentagram Map
Integrability Pentagram Map R. Schwartz convex planar polygons
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2011/7/7
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...
Integrability of weak distributions on Banach manifolds
Banach manifold weak Banach submanifold weak distribution integral manifold
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2011/1/19
This paper concerns the problem of integrability of non closed distributions on Banach
manifolds. We introduce the notion of weak distribution and we look for conditions under
which these distributi...
On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory
Differential Galois Theory Darboux theory of Integrability Poincar´ e problem,
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2011/2/24
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type folia-tion.
A geometric approach to integrability of Abel differential equations
Abel equation Lie systems Jacobi multiplier
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2011/1/20
A geometric approach is used to study the Abel first order differential equation of the first kind. The approach is based on the recently developed theory of quasi-Lie systems which allows us to chara...
Integrability and chaos: the classical uncertainty
Integrability and chaos classical uncertainty
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2010/12/28
In recent years there has been a considerable increase in the publishing of textbooks and mono-
graphs covering what was formerly known as random or irregular deterministic motion, now named
by the ...
The AKNS Hierarchy Integrability Analysis Revisited: The Vertex Operator Approach and its Lie-Algebraic Structure
the AKNS hierarchy Lax type integrability Lie-algebraic approach
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2011/3/2
A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised.