共查询到19条相似文献,搜索用时 109 毫秒
1.
本文研究高维退化系统在小扰动下的动力学行为,在共振的情况下,利用延拓的方法,讨论了扰动系统不变环面的保存性,并利用推广的Melnikov函数、横截性理论讨论了同宿于不变环面的横截同宿轨道存在的条件,推广和改进了一些文献的结果. 相似文献
2.
非 Hamilton 系统的次谐分叉和马蹄 总被引:1,自引:0,他引:1
目前,浑沌理论引起了人们广泛的兴趣,已有一系列理论的结果.判断浑沌的发生通常是检验横截同宿点的存在.最近,严寅、钱敏证明了:对于异宿点,若具有横截 n-环,则同样存在 Smal 马蹄.对于二维的 Hamilton 系统受扰动后,Melnikov 给出了判定 Poincaré映射横截同宿点或异宿点存在的解析工具.本文讨论非 Hamilton 系统:=uv,(?)=1-u~2-v~2在适当的扰动下存在 Smal 马蹄,同时,用 Melnikov 方法讨论了次谐分叉及次谐分叉与马蹄的关系. 相似文献
3.
用指数二分法,横截性理论和推广的Melnikov方法,来研究具有较高退化程度的异宿、同宿轨在扰动下保存和横截的条件,结果推广、包含和改进了许多重要文献的结果。 相似文献
4.
本文讨论辛映射的扰动问题.利用修改的ArnoldKAM迭代格式,给出一个不变环面的保持性定理.由于可积映射具有退化性,这推广了文[6]的工作. 相似文献
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对一类奇异摄动系统中由奇异极限环产生的不变环面分支进行了研究并利用不变环面的分支理论,讨论了由快系统的二重极限环和三重环分支出的不变环面的存在性. 相似文献
7.
对一类奇异摄动系统中由奇异极限环产生的不变环面分支进行了研究并利用不变环面的分支理论,讨论了由快系统的二重极限环和三重环分支出的不变环面的存在性. 相似文献
8.
讨论一类三维自治系统的闭轨在周期扰动下的分支问题.利用Poincare映射与积分流形定理,得到扰动系统存在次调和解和不变环面的条件,以及次调和解的鞍结点分支. 相似文献
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讨论一类三维系统在周期扰动下的分支问题.假设此三维系统有一族闭轨,利用 Poincar\'e映射及积分流形定理,得到了在周期扰动下由这族闭轨产生次调和解和不变环面的条件,并讨论了次调和解的鞍结点分支. 相似文献
11.
We consider perturbations of integrable Hamiltonian systems in the neighbourhood of normally umbilic invariant tori. These lower dimensional tori do not satisfy the usual non-degeneracy conditions that would yield persistence by an adaption of KAM theory, and there are indeed regions in parameter space with no surviving torus. We assume appropriate transversality conditions to hold so that the tori in the unperturbed system bifurcate according to a (generalised) umbilical catastrophe. Combining techniques of KAM theory and singularity theory we show that such bifurcation scenarios of invariant tori survive the perturbation on large Cantor sets. Applications to gyrostat dynamics are pointed out. 相似文献
12.
设M和N是Cr (r≥1) Banach流形, P\subset N 是N的子流形, f是从M 到N的C1映射. 该文引进映射f在x0∈f-1(P)点 与P广义横截的概念,它是经典的横截概念的推广. 接着讨论了广义横截性和广义正则点的关系,证明:映射f在x0点与P广义横截的充分必要条件为 x0是与f相关的某个映射g 的广义正则点; 当子流形$P$退化成单点集时,若映射 f与P={p}广义横截, 作者证明p是f的广义正则值; 最后 证明了广义横截点的全体O={x∈ f-1(P): f\pitchfork_G^x P} 是开集. 相似文献
13.
Consider the time-periodic perturbations of an n-dimensional autonomous system with a nonhyperbolic closed orbit in the phase space. By the method of averaging and Floquet theory, the bifurcations of the invariant torus in the extended phase space are studied. 相似文献
14.
1IntroductionTheproblems0finvarianttorusbifurcationforplanarHamilt0niansy-stemshavebeenextensivelystudiedandmanyresultshavebeen0btained(see[l-4]andthereferencestherein).However,theresultsconcernedwiththeinvarianttorusbifurcati0n0fhigherdimensi0nalsystemsarestillrelativelyfew.Recentlyann-dimensi0nalsystem,whichhasanormallyhyperbolicin-variantmanif0ldconsistingentirely0fclosedorbits,wasconsidered,andtheexistenceandthenormalhyperbolicityoftheinvariantt0rusweregivenin[5].Paper[6]extendedthesystem… 相似文献
15.
Daniel Stoffer 《Numerische Mathematik》1997,77(4):535-547
Summary. We consider a dissipative perturbation of non–resonant harmonic oscillators. Under the perturbation the system admits a weakly
attractive invariant torus. We apply a Runge-Kutta method to the system. If the integration method is symplectic then it also
admits an attractive invariant torus, the step-size being independent of the perturbation parameter. For non–symplectic methods
the discrete system only admits an attractive invariant torus if the step-size is so small such that the discretisation error
is smaller than the perturbation.
Received May 17, 1996 相似文献
16.
K. Yagasaki 《Journal of Nonlinear Science》1999,9(1):131-148
Summary. We study a two-frequency perturbation of Duffing's equation. When the perturbation is small, this system has a normally hyperbolic
invariant torus which may be subjected to phase locking. Applying a version of Melnikov's method for multifrequency systems,
we detect the occurrence of transverse intersection between the stable and unstable manifolds of the invariant torus. We show
that if the invariant torus is not subjected to phase locking, then such a transverse intersection yields chaotic dynamics.
When the invariant torus is subjected to phase locking, the situation is different. In this case, there exist two periodic
orbits which are created in a saddle-node bifurcation. Using another version of Melnikov's method for slowly varying oscillators,
we also give conditions under which the stable and unstable manifolds of the periodic orbits intersect transversely and hence
chaotic dynamics may occur. Our results reveal that when the invariant torus is subjected to phase locking, chaotic dynamics
resulting from transverse intersection between its stable and unstable manifolds may be interrupted.
Received November 18, 1993; final revision received September 9, 1997; accepted October 27,1997 相似文献
17.
In Bataineh (2003) [2] we studied the type one invariants for knots in the solid torus. In this research we study the type one invariants for n-component links in the solid torus by generalizing Aicardi's invariant for knots in the solid torus to n-component links in the solid torus. We show that the generalized Aicardi's invariant is the universal type one invariant, and we show that the generalized Aicardi's invariant restricted to n-component links in the solid torus with zero winding number for each component is equal to an invariant we define using the universal cover of the solid torus. We also define and study a geometric invariant for n-component links in the solid torus. We give a lower bound on this invariant using the type one invariants, which are easy to calculate, which helps in computing this geometric invariant, which is usually hard to calculate. 相似文献
18.
We establish sufficient conditions for the differentiability of the invariant torus of a countable system of linear difference equations defined on a finite-dimensional torus with respect to an angular variable and the parameter of the original system of equations. 相似文献