Results 1 to 10 of about 1,641 (211)
Homoclinic Orbits and Lagrangian Embeddings [PDF]
International Mathematics Research Notices, 2008 This paper introduces techniques of symplectic topology to the study of homoclinic orbits in Hamiltonian systems. The main result is a strong generalization of homoclinic existence results due to Sere and to Coti-Zelati, Ekeland and Sere, which were obtained by variational methods.
Samuel Lisi
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On homoclinic and heteroclinic orbits for Hamiltonian systems [PDF]
Differential and Integral Equations, 1997 The authors give sufficient conditions for the existence of homoclinic and heteroclinic orbits of Hamiltonian systems \[ u''-L(t)u+V_u(t,u)=0,\tag{*} \] where \(L\) is a symmetric positive definite \(n\times n\) matrix and the potential \(V\) is supposed to be superquadratic in \(u\).
Philip Korman, A. C. Lazer, Yi Li
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Existence and Multiplicity of Homoclinic Orbits for Second-Order Hamiltonian Systems with Superquadratic Potential [PDF]
Abstract and Applied Analysis, 2013 We investigate the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems with local superquadratic potential by using the Mountain Pass Theorem and the Fountain Theorem, respectively.
Ying Lv, Chun-Lei Tang
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Periodic and homoclinic orbits in a toy climate model [PDF]
Nonlinear Processes in Geophysics, 1994 A two dimensional system of autonomous nonlinear ordinary differential equations models glacier growth and temperature changes on an idealized planet.
M. Toner, A. D. Kirwan, Jr.
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Homoclinic Orbits in Families of Hypersurfaces with Hyperbolic Periodic Orbits
Journal of Differential Equations, 2002 The author considers the Hamiltonian system \(\dot{X}=J\nabla H(X)\) on \(\mathbb{C}^n\) with a \(C^2\)-Hamiltonian \(H:\mathbb{C}^n\to\mathbb{R}\). Here \(J\) induces the standard symplectic structure on \(\mathbb{C}^n\). Denote \(X=(x,y)\in\mathbb{C}\times\mathbb{C}^{n-1}\).
Patrick Bernard
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Existence of Homoclinic Orbits for Hamiltonian Systems with Superquadratic Potentials [PDF]
Abstract and Applied Analysis, 2009 This paper concerns solutions for the Hamiltonian system: z˙=𝒥Hz(t,z). Here H(t,z)=(1/2)z⋅Lz+W(t,z), L is a 2N×2N symmetric matrix, and W∈C1(ℝ×ℝ2N,ℝ).
Jian Ding, Junxiang Xu, Fubao Zhang
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Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian System [PDF]
MATEC Web of Conferences, 2016 In this study, we develop the energy-phase method to deal with the high-dimensional non-autonomous nonlinear dynamical systems. Our generalized energy-phase method applies to integrable, two-degree-of freedom non-autonomous resonant Hamiltonian systems ...
Zhou Sha, Zhang Wei, Yu Tian-jun
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Homoclinic orbits for a class of $p$-Laplacian systems with periodic assumption
Electronic Journal of Qualitative Theory of Differential Equations, 2013 In this paper, by using a linking theorem, some new existence criteria of homoclinic orbits are obtained for the $p$-Laplacian system $d(|\dot{u}(t)|^{p-2}\dot{u}(t))/dt+\nabla V(t,x)=f(t)$, where $p>1$, $V(t,x)=-K(t,x)+W(t,x)$.
Xingyong Zhang
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Bifurcation of big periodic orbits through symmetric homoclinics, application to Duffing equation [PDF]
Journal of Mahani Mathematical Research, 2023 We consider a planar symmetric vector field that undergoes a homoclinic bifurcation. In order to study the existence of exterior periodic solutions of the vector field around broken symmetric homoclinic orbits, we investigate the existence of fixed ...
Liela Soleimani, Omid RabieiMotlagh
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Mathematics, 2021 The existence of homoclinic orbits or heteroclinic cycle plays a crucial role in chaos research. This paper investigates the existence of the homoclinic orbits to a saddle-focus equilibrium point in several classes of three-dimensional piecewise affine ...
Yanli Chen, Lei Wang, Xiaosong Yang
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