Intersection of Stable and Unstable Manifolds for Invariant Morse Function
نویسندگان
چکیده
منابع مشابه
Stable manifolds for an orbitally unstable NLS
By this we mean that φ > 0 and φ ∈ C2(R3). It is a classical fact (see Coffman [Cof]) that such solutions exist and are unique for the cubic nonlinearity. Moreover, they are radial and smooth. Similar facts are known for more general nonlinearities, see e.g., Berestycki and Lions [BerLio] for existence and Kwon [Kwo] for uniqueness in greater generality. Clearly, ψ = eitα 2 φ solves (1). We see...
متن کاملThe Intersection Angles between N-Dimensional Stable and Unstable Manifolds in 2N-Dimensional Symplectic Mappings
We asymptotically compute the intersection angles between N -dimensional stable and unstable manifolds in 2N -dimensional symplectic mappings. There exist particular 1-dimensional stable and unstable sub-manifolds which experience exponentially small splitting of separatrix in our models. We show that the angle between the sub-manifolds is exponentially small with respect to the perturbation pa...
متن کاملApproximating stable and unstable manifolds in experiments.
We introduce a procedure to reveal invariant stable and unstable manifolds, given only experimental data. We assume a model is not available and show how coordinate delay embedding coupled with invariant phase space regions can be used to construct stable and unstable manifolds of an embedded saddle. We show that the method is able to capture the fine structure of the manifold, is independent o...
متن کاملNumerical Computation of the Stable and Unstable Manifolds of Invariant Tori
We develop an iterative technique for computing the unstable and stable eigenfunctions of the invariant tori of diffeomorphisms. Using the approach of Jorba, the linearized equations are rewritten as a generalized eigenvalue problem. Casting the system in this light allows us to take advantage of the speed of eigenvalue solvers and create an efficient method for finding the first order approxim...
متن کاملStable and Unstable Manifolds for Planar Dynamical Systems
An introduction to the qualitative study of planar systems of nonlinear ordinary differential equations is typically encountered at the junior or senior year in a second course in differential equations. These courses are becoming increasingly popular, due to the widespread use of inexpensive computer software which allows the student to experiment very early on in the learning process and beca...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 2013
ISSN: 0387-3870
DOI: 10.3836/tjm/1391177985