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Melnikov’s method in String Theory [PDF]
Journal of High Energy Physics, 2016 37 pages, 5 ...
Asano, Yuhma +2 more
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Melnikov’s method for chaos of the nanoplate postulating nonlinear foundation
Applied Mathematical Modelling, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Xiaohua, Zhou, Liangqiang
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Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems [PDF]
Journal of Mathematical Physics, 1982 We start with an unperturbed system containing a homoclinic orbit and at least two families of periodic orbits associated with action angle coordinates. We use Kolmogorov–Arnold–Moser (KAM) theory to show that some of the resulting tori persist under small perturbations and use a vector of Melnikov integrals to show that, under suitable hypotheses ...
Holmes, Philip J., Marsden, Jerrold E.
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Melnikov's Method and Codimension-Two Bifurcations in Forced Oscillations
Journal of Differential Equations, 2002 The author considers a periodic perturbation of a planar Hamiltonian system of the form \[ \dot{x}=JD_x H(x)+\epsilon g(x,\omega t;\mu),\qquad x\in \mathbb{R}^2. \] It is assumed that the unperturbed system has a one-parameter family of periodic orbits \(q^{\alpha}(t)\) analytic with respect to \(\alpha\).
K. Yagasaki
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Application of Melnikov's Method to the Reduced KdV Equation
Australian Journal of Physics, 1991 The Melnikov method for estimating distances between invariant manifolds is applied to the perturbed system of ordinary differential equations obtained from the KdV equation, reduced by a travelling wave ansatz and including a diffusion term. The calculation is performed after one integration and the result is compared with numerical work carried out ...
J. Roessler
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Beyond the Melnikov method II: Multidimensional setting [PDF]
Journal of Differential Equations, 2018 25 ...
Maciej J. Capiński, Piotr Zgliczyński
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A Melnikov Method for Homoclinic Orbits with Many Pulses [PDF]
Archive for Rational Mechanics and Analysis, 1998 The authors study the persistence of homoclinic orbits with many pulses for hyperbolic periodic orbits to a system being a perturbation of a four-dimensional integrable Hamiltonian system. The unperturbed system is supposed to have a one-parameter family of hyperbolic periodic orbits, such that stable and unstable manifolds of each periodic orbit ...
Kovačič, Gregor +2 more
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Singular Separatrix Splitting and the Melnikov Method: An Experimental Study [PDF]
Experimental Mathematics, 1999 We consider families of analytic area-preserving maps depending on two pa- rameters: the perturbation strength E and the characteristic exponent h of the origin. For E=0, these maps are integrable with a separatrix to the origin, whereas they asymptote to flows with homoclinic connections as h->0+.
Delshams, Amadeu, Ramírez-Ros, Rafael
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Beyond the Melnikov method: A computer assisted approach
Journal of Differential Equations, 2017 We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds (NHIMs). The method is based on a new geometric proof of the normally hyperbolic invariant manifold theorem, which establishes the existence of a NHIM, together with its associated invariant ...
Capiński, Maciej J. +1 more
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The Melnikov Method and Subharmonic Orbits in a Piecewise-Smooth System [PDF]
SIAM Journal on Applied Dynamical Systems, 2012 In this work we consider a two-dimensional piecewise smooth system, defined in two domains separated by the switching manifold $x=0$. We assume that there exists a piecewise-defined continuous Hamiltonian that is a first integral of the system. We also suppose that the system possesses an invisible fold-fold at the origin and two heteroclinic orbits ...
Albert Granados +2 more
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