Results 21 to 30 of about 1,641 (211)
Homoclinic orbit to a center manifold [PDF]
Calculus of Variations and Partial Differential Equations, 2003 Homoclinic orbit to a center manifold are obtained with a variational method.
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Continuation of Homoclinic Orbits in Matlab [PDF]
, 2005 We have added the functionality for continuing homoclinic orbits to cl_matcont, a user-friendly matlab package for the study of dynamical systems and their bifurcations. It is now possible to continue homoclinic-to-hyperbolic-saddle and homoclinic-to-saddle-node orbits.
Willy Govaerts +3 more
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Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space
Abstract and Applied Analysis, 2011 This paper is concerned with distribution of maps with transversal homoclinic orbits in a continuous map space, which consists of continuous maps defined in a closed and bounded set of a Banach space.
Qiuju Xing, Yuming Shi
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Homoclinic orbits for periodic second order Hamiltonian systems with superlinear terms
Electronic Journal of Qualitative Theory of Differential Equations, 2022 We obtain the existence of nontrivial homoclinic orbits for nonautonomous second order Hamiltonian systems by using critical point theory under some different superlinear conditions from those previously used in Hamiltonian systems.
Haiyan Lv, Guanwei Chen
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Homoclinic orbits for Schrödinger systems
Michigan Mathematical Journal, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Schechter, Martin, Zou, Wenming
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Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria
The Scientific World Journal, 2014 The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip ...
Fengjie Geng, Junfang Zhao
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Homoclinic orbits of sub-linear Hamiltonian systems with perturbed terms
Boundary Value Problems, 2021 By using variational methods, we obtain the existence of homoclinic orbits for perturbed Hamiltonian systems with sub-linear terms. To the best of our knowledge, there is no published result focusing on the perturbed and sub-linear Hamiltonian systems.
Haiyan Lv, Guanwei Chen
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Pseudoholomorphic curves and multiplicity of homoclinic orbits [PDF]
Duke Mathematical Journal, 1995 The authors consider a Hamiltonian system of the form \[ \dot x = J(x) H'(t;x) \tag{1} \] on a compact, smooth Riemannian manifold \(M\). The function \(H : \mathbb{R} \times TM \to \mathbb{R}\) is smooth, 1-periodic in time and admits a point \(q_0 \in M\) such that \[ H(t; q_0, 0) = 0,\quad H'(t;q_0, 0) = 0, \] \[ H(t; q_0, p) \geq 0,\quad H(t;q,0) <
Cieliebak, Kai, Séré, Eric
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Abstract and Applied Analysis, 2013 We study a class of nonperiodic damped vibration systems with asymptotically quadratic terms at infinity. We obtain infinitely many nontrivial homoclinic orbits by a variant fountain theorem developed recently by Zou.
Guanwei Chen
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A Numerical Bifurcation Function for Homoclinic Orbits [PDF]
SIAM Journal on Numerical Analysis, 1998 Summary: The authors present a numerical method to locate periodic orbits near homoclinic orbits. Using a method of [\textit{X.-B. Lin}, Proc. R. Soc. Edinb., Ser. A 116, 295-325 (1990; Zbl 0714.34070)] and solutions of the adjoint variational equation, one gets a bifurcation function for periodic orbits, whose periods are asymptotic to infinity on ...
Ashwin, Peter, Mei, Zhen
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