DYNAMICAL_SYSTEM

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Fast-slow stochastic dynamical system with singular coefficients
《Science China Mathematics》2023年第4期819-838,共20页Longjie Xie 
supported by the Alexander von Humboldt foundation and National Natural Science Foundation of China(Grant Nos.12090011,12071186 and 11931004)。
This paper aims to study the asymptotic behavior of a fast-slow stochastic dynamical system with singular coefficients,where the fast motion is given by a continuous diffusion process while the slow component is drive...
关键词：multi-scale dynamical system averaging principle central limit theorem α-stable process Zvonkin’s transformation 
Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation
《Science China Mathematics》2022年第2期291-308,共18页Qian Yang Mingkang Ni 
supported by National Natural Science Foundation of China(Grant No.11871217);the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000)。
A piecewise-smooth second-order singularly perturbed differential equation whose right-hand side is a nonlinear function with a discontinuity on some curve is investigated. This is a new class of problems in the case ...
关键词：reaction-diffusion equation multizonal internal layer asymptotic method piecewise-smooth dynamical system 
Searching the solution landscape by generalized high-index saddle dynamics被引量：4
《Science China Mathematics》2021年第8期1801-1816,共16页Jianyuan Yin Bing Yu Lei Zhang 
supported by National Natural Science Foundation of China(Grant No.11861130351);the support from the Elite Program of Computational and Applied Mathematics for Ph D Candidates of Peking University。
We introduce a generalized numerical algorithm to construct the solution landscape,which is a pathway map consisting of all the stationary points and their connections.Based on the high-index optimizationbased shrinki...
关键词：saddle point energy landscape solution landscape pathway map dynamical system phase field 
Topologically conjugate classifications of the translation actions on low-dimensional compact connected Lie groups
《Science China Mathematics》2021年第5期963-1010,共48页Xiaotian Pan Bingzhe Hou 
In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of SU(2), U(2), SO(3), SO(3)×S^(1) and Spin ^(C)(3). We define th...
关键词：topological conjugacy rotation vectors translation actions C~*-dynamical system classification 
Shrinking target problems for beta-dynamical system被引量：3
《Science China Mathematics》2013年第1期91-104,共14页SHEN LuMing WANG BaoWei 
supported by National Natural Science Foundation of China(Grant Nos.10901066 and 51149008);Hunan Natural Science Foundation(Grant No.09JJ3001)
For any β 〉 1, let （[0, 1],Tβ） be the beta dynamical system. For a positive function ψ ： N → R＋ and a real number x0 E [0, 1], we define D（Tβ, ψ, xo） the set of ψ-well approximable points by xo as {x C [...
关键词：β -dynamical system shrinking target problems Hausdorff dimension 
Quantitative Poincar recurrence in continued fraction dynamical system被引量：3
《Science China Mathematics》2012年第1期131-140,共10页PENG Li TAN Bo WANG BaoWei 
supported by National Natural Science Foundation of China (Grant Nos.10631040,10901066)
Let T ： X → X be a transformation. For any x C [0, 1） and r 〉 O, the recurrence time Tr（x） of x under T in its r-neighborhood is defined as Tr（X） = inf{k ≥ 1： d（Tk（x）,x） 〈 r}.For 0 ≤ α ≤ β ∞ co, le...
关键词：RECURRENCE continued fraction Hausdorff dimension 
Dependent sets of a family of relations of full measure on a probability space被引量：1
《Science China Mathematics》2007年第4期475-484,共10页Jin-cheng XIONG Feng TAN Jie Lü 
This work was supported by the National Science Fbundation of China (Grant No. 10471049)
For a probability space (X, B, μ) a subfamily F of the σ-algebra B is said to be a regular base if every B ∈ B can be arbitrarily approached by some member of F which contains B in the sense of the measure theory. ...
关键词：probability space measure-preserving transformation dependent set chaos dynamical system 28A12 28A35 37A05 
On the Stability and Control of Dynamical System With Flexible Structure
《Science China Mathematics》1993年第1期36-47,共12页王照林 徐建国 
Project supported by the National Natural Science Foundation of China and Astronautics Ministry
In this paper the stability and control of complex dynamic system with elastic structure are investigated. As the dynamic model of the system is described by the coupled system of ordinary differential equations and p...
关键词：ELASTIC vibration DYNAMICAL system spectrum theory SEMIGROUP of OPERATOR stability control. 
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