Results 11 to 20 of about 8,908 (255)
Homoclinic Orbits In Slowly Varying Oscillators [PDF]
SIAM Journal on Mathematical Analysis, 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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Scarring by homoclinic and heteroclinic orbits [PDF]
Physical Review Letters, 2006 In addition to the well known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when associated ...
A. M. Ozorio de Almeida +7 more
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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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Are physiological oscillations physiological?
The Journal of Physiology, EarlyView., 2023 Abstract figure legend Mechanisms and functions of physiological oscillations. Abstract Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function.
Lingyun (Ivy) Xiong, Alan Garfinkel
wiley +1 more source
On the Homoclinic Orbits of the Lü System [PDF]
International Journal of Bifurcation and Chaos, 2017 In this paper, the existence of homoclinic orbits of the equilibrium point [Formula: see text] is demonstrated in the case of the Lü system for parameter values not reported by G. A. Leonov. In addition, some simulations are shown that agree with our theoretical analysis.
Álvarez-Ramírez, Martha +1 more
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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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Homoclinic orbits to invariant tori near a homoclinic orbit to center–center–saddle equilibrium [PDF]
Physica D: Nonlinear Phenomena, 2005 We consider a perturbation of an integrable Hamiltonian vector field with three degrees of freedom with a center–center–saddle equilibrium having a homoclinic orbit or loop. With the help of a Poincaré map (chosen based on the unperturbed homoclinic loop), we study the homoclinic intersections between the stable and unstable manifolds associated to ...
Koltsova, Oksana +3 more
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An example of bifurcation to homoclinic orbits
Journal of Differential Equations, 1980 AbstractConsider the equation ẍ − x + x2 = −λ1x + λ2ƒ(t) where ƒ(t + 1) = ƒ(t) and λ = (λ1, λ2) is small. For λ = 0, there is a homoclinic orbit Γ through zero. For λ ≠ 0 and small, there can be “strange” attractors near Γ. The purpose of this paper is to determine the curves in λ-space of bifurcation to “strange” attractors and to relate this to ...
Shui-Nee Chow +2 more
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Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics [PDF]
, 2000 In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem.
Koon, Wang Sang +3 more
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