Titlebook: Hamiltonian Systems with Three or More Degrees of Freedom; Carles Simó Book 1999 Springer Science+Business Media Dordrecht 1999 Kolmogorov

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https://doi.org/10.1007/978-1-349-17853-7One of the first methods to compute quasi-periodic orbits (i. e. invariant tori with linear motions on them) was the Lindstedt method (see [14] Vol. 2) which produces an expansion of the quasi-periodic orbit with a fixed frequency in powers of a small parameter measuring the distance to integrability.

Connotation

Inflection Points, Extatic Points and Curve ShorteningIf (..,.) is a surface with Riemannian metric, then a family of immersed curves .. | 0 ≤ . < . on .. evolves by . if where .. is the geodesic curvature, and . is a unit normal to the curve. Since ... can be written as where . is arclength along ., (1) is essentially a parabolic equation, i.e. a nonlinear heat equation.

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Heteroclinic Chains of Skew Product Hamiltonian SystemsConsider a time dependent Hamiltonian system.with configuration manifold . and phase space.Here .: . → ... is the operator corresponding to the symplectic structure . ∧ . Fix a complete Riemannian metric ∥ ? ∥ on .. Let . satisfy the following assumptions.

vector

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On The Discrete One-Dimensional Quasi-Periodic Schr?dinger Equation and Other Smooth Quasi-Periodic In this paper we shall review some results about . and some other skew products over a . of the one-dimensional torus T = ?/(2π?). The results are of perturbation character and obtained by KAM-type arguments.

思想上升

Lindstedt Series for Lower Dimensional ToriOne of the first methods to compute quasi-periodic orbits (i. e. invariant tori with linear motions on them) was the Lindstedt method (see [14] Vol. 2) which produces an expansion of the quasi-periodic orbit with a fixed frequency in powers of a small parameter measuring the distance to integrability.

Torrid

https://doi.org/10.1007/978-3-031-63083-5 of the three body problem, [1], In modern language, [2], it is the generating function, that I call . here, . of the sequence of trigonometric polynomials associated with well known combinatorial objects, namely ..

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