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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On several bi-Hamiltonian systems
双哈密顿系统 齐次Hamitionan算子 相容三元组
2023/11/13
Recently, based on the classification of the second and third order homogeneous Hamitionan operators Lorenzoni and his collaborators classified compatible trios of two-component homogeneous Hamiltonia...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Higher-order Hamiltonian generalization evolution equations
高阶 哈密顿 广义演化方程
2023/11/13
In this talk, I will review several classes of higher-order generalizations of the integrable Camassa-Holm equation in the Hamiltonian forms. Then, I talk about some new results for one generalized Ca...
Workshop on Dynamics and integrability of nonholonomic and other non-Hamiltonian systems
Workshop Dynamics and integrability of nonholonomic and other non-Hamiltonian systems
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...
2018哈密顿动力学与辛拓扑最新进展研讨会（Recent Advances in Hamiltonian Dynamics and Symplectic Topology Workshop）
2018 哈密顿动力学与辛拓扑最新进展 研讨会
2017/12/20
The study of Hamiltonian dynamical systems plays a fundamental role in many different contexts, both in pure and applied mathematics. Indeed, most of the physical laws ruling our everyday lives --the ...
A PRIORI ESTIMATES FOR MANY-BODY HAMILTONIAN EVOLUTION OF INTERACTING BOSON SYSTEM
Dispersive estimates interaction Morawetz type (correlation) estimates many-body Hamiltonian many-body Schrodinger equation quantum hydrodynamics BBGKY hierarchy
2015/10/16
We study the evolution of a many-particle system whose wave function obeys the N-body Schr¨ odinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the...
AVERAGING OF HAMILTONIAN FLOWS WITH AN ERGODIC COMPONENT
ERGODIC COMPONENT Unperturbed flow
2015/9/29
We consider a process on T2, which consists of fast motion along the
stream lines of an incompressible periodic vector field perturbed by white
noise. It gives rise to a process on the graph n...
Invariant functions on Lie groups and Hamiltonian flows ofsurface group representations
Lie groups Hamiltonian flows
2015/9/29
In [7] it wasshown that ifn isthe fundamental group ofa closed oriented surface S
and Gis Lie group satisfying very general conditions, then the space Hom(n, G)/G
of conjugacy classes of representat...
Averaging of Hamiltonian Flows with an Ergodic Component
Rapid movement white noise the vector field perturbation function
2015/9/28
We consider a process on T 2, which consists of the fast motion along the stream lines of an incompressible periodic vector field perturbed by white noise. It gives rise to a process on the grap...
An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension
Nearly Integrable Hamiltonian System Trajectory Dense Maximal Hausdorff Dimension
2015/9/25
The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it.Ehrenfest (The Conceptual Foundations of th...
A note on micro-instability for Hamiltonian systems close to integrable
micro-instability Hamiltonian systems close to integrable
2015/9/25
In this note, we consider the dynamics associated to a perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following resul...
Dynamics of the dominant Hamiltonian,with applications to Arnold diffusion
dominant Hamiltonian Arnold diffusion
2015/9/25
It is well know that instabilities of nearly integrable Hamiltonian systems occur around resonances. Dynamics near resonances of these systems is wellapproximated by the associated averaged system, ca...
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The ...
Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit
Index and Stability of Symmetric Periodic Orbits Hamiltonian Systems Application to Figure-Eight Orbit
2015/4/3
Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit.
Shilnikov Lemma for a normally hyperbolic critical manifold of a Hamiltonian system
Shilnikov Lemma normally hyperbolic critical manifold Hamiltonian system
2015/3/18
Shilnikov Lemma for a normally hyperbolic critical manifold of a Hamiltonian system.
Effective Hamiltonian in the Problem of a "Central Spin" Coupled to a Spin Environment
Spin quantum interactive microcosmic spin micro rotation magnetic particles low-energy properties model
2014/12/23
We consider here the problem of a "giant spin", with spin quantum number S≫1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model desc...