A note on the Melnikov function [PDF]
Vietnam Journal of Mechanics, 2007 With one (Poincaré section) parameter and a particular motion law (that associated to certain determined point of horno-heteroclinic orbits), the usual form of the Melnikov function seems to be not convenient for certain problems. Another favorable form can be obtained by using a supplementary parameter - the arbitrary time constant in the general ...
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Bifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems
Abstract and Applied Analysis, 2012 The bifurcations near a primary homoclinic orbit to a saddle-center are investigated in a 4-dimensional reversible system. By establishing a new kind of local moving frame along the primary homoclinic orbit and using the Melnikov functions, the existence
Zhiqin Qiao, Yancong Xu
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Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio [PDF]
, 2014 We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly-integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is
A Delshams +35 more
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Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle
Abstract and Applied Analysis, 2014 We study the expansions of the first order Melnikov functions for general near-Hamiltonian systems near a compound loop with a cusp and a nilpotent saddle.
Huanhuan Tian, Maoan Han
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Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order 2
上海师范大学学报. 自然科学版, 2018 Determining the number of limit cycles of a planar differential system is related to the second part of Hilbert's 16th problem. In this paper, a near-Hamiltonian system is studied, where the unperturbed system has a double homoclinic loop with second ...
Tian Huanhuan
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Nonlinear Dynamics of Accelerator via Wavelet Approach [PDF]
, 1997 In this paper we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems.
Fedorova, Antonina N. +1 more
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Morse and Melnikov functions for NLS Pde's [PDF]
Communications in Mathematical Physics, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Y., McLaughlin, David W.
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On the class SI of J-contractive functions intertwining solutions of linear differential equations [PDF]
, 2010 In the PhD thesis of the second author under the supervision of the third author was defined the class SI of J-contractive functions, depending on a parameter and arising as transfer functions of overdetermined conservative 2D systems invariant in one ...
A. Melnikov +19 more
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Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold
, 2018 We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family.
Bastos, Jéfferson L. R. +3 more
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Homoclinic Orbits In Slowly Varying Oscillators [PDF]
, 1987 We obtain existence and bifurcation theorems for homoclinic orbits in three-dimensional flows that are perturbations of families of planar Hamiltonian systems. The perturbations may or may not depend explicitly on time.
Holmes, Philip, Wiggins, Stephen
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