homoclinic point 中文意思是什麼
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Within the homoclinic orbit or heteroclinic orbit, the analytical expression of one set of periodical track surrounding the center - type singular point is worked out
得到了同宿軌道或異宿軌道內的，圍繞中心型奇點的一族周期軌道的解析表達式。 -
Every result in the paper is presented through specific analytic expression, including the analytic expression of homoclinic orbit or heteroclinic orbit and its melnikov function, analytical expression of periodical track surrounding the center - type singular point within the homoclinic orbit or heteroclinic orbit and its melinkov function, the critical value when periodical m point appears, the critical value when smale horseshoes chaos appears, etc.
文中的各個結果均以具體的解析形式給出，其中包括同宿軌道或異宿軌道的解析表達式及其melnikov函數；同（異）宿軌道內圍繞中心型奇點的周期軌道的解析表達式及其melnikov函數；出現周期m點的臨界值；出現smale馬蹄混沌的臨界值等。 -
Nature of the singular point of plane poincare mapping that is established by equation ( 1 ) is analyzed. relationship between the three parameters and homoclinic orbit and heteroclinic orbit of the hamilton system corresponding to this sort of equation is discussed. the adequate and essential condition of the existing homoclinic orbit or heteroclinic orbit for the hamilton system is presented
分析了方程（ 1 ）建立的平面poincare映射的奇點性質，討論了此類方程對應的hamilton系統的同宿軌道和異宿軌道與三個參數o 、夕、屍的關系，給出了hamilton系統存在同宿軌道或異宿軌道的充分必要條件。 -
By virtue of the stochastic bifurcation theory, the transition of the atom movement at a crack tip in fatigue damage system is investigated. using the singular point theory of one - dimensional diffusion process and the stochastic averaging approach of energy envelope, a micro - model to describe the atom movement at the crack tip in homoclinic bifurcation fatigue damage system, which is in the presence of stochastic perturbation, is established. after the study on the characteristic of the diffusion exponent, the drift exponent and the character exponent of the fatigue damage diffusion process on singular boundary, the bifurcation behavior of a homoclinic bifurcation fatigue damage system, which is in the presence of parametric white noise, is examined
採用隨機分叉理論，探討疲勞損傷系統裂尖粒子運動性質突變.利用一維擴散過程的奇點理論，並結合能量包絡的隨機平均法，建立了隨機擾動的疲勞損傷同宿分叉系統裂尖粒子運動模型，通過研究奇異邊界的擴散指數、漂移指數以及特徵指數特性，考查疲勞損傷裂尖粒子運動的同宿分叉系統受參激白噪聲影響的分叉行為 -
In section 2, we study the fixed point, stable set and unstable set of this system. for given parameters a trapping region is found with the property that any interval of unstable set will be expand under the map, so we get the conclusion that the system has infinitely many homoclinic orbits. as a consequence of the previous conclusion, we discuss the attractor of the system
在本文中，我們討論了一個分段線性模型，它是物理學中用來模擬r - l - diode電路行為的數學方程，通過研究，我們得到該系統的一些拓撲性質以及符號動力學中的一些結論，主要內容如下：在第二節中，我們對給定的參數值，通過數值計算研究了該系統的不動點，不動點附近的穩定集與不穩定集，發現該系統中存在一個捕捉區域：該區域中的不穩定流形總體上是擴張的。
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