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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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Heteroclinic Orbits for a Discrete Pendulum Equation [PDF]
Journal of Difference Equations and Applications, 2010 About twenty years ago, Rabinowitz showed firstly that there exist heteroclinic orbits of autonomous Hamiltonian system joining two equilibria. A special case of autonomous Hamiltonian system is the classical pendulum equation.
Xiao, Huafeng, Yu, Jianshe
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Index theory for heteroclinic orbits of Hamiltonian systems [PDF]
, 2017 Index theory revealed its outstanding role in the study of periodic orbits of Hamiltonian systems and the dynamical consequences of this theory are enormous.
Hu, Xijun, Portaluri, Alessandro
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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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Existence of Heteroclinic Orbits in Fractional-Order and Integer-Order Coupled Lorenz Systems
Fractal and FractionalApplying two Lyapunov functions and the concepts of α-/ω-limit sets, this paper reexamines fractional-order and integer-order coupled Lorenz systems and simultaneously proves the existence of twelve heteroclinic orbits, i.e., four ones to S0 and S5,6,7,8,
Guiyao Ke +3 more
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Globally Exponentially Attracting Sets and Heteroclinic Orbits Revealed [PDF]
MathematicsMotivated by the open problems on the global dynamics of the generalized four-dimensional Lorenz-like system, this paper deals with the existence of globally exponentially attracting sets and heteroclinic orbits by constructing a series of Lyapunov ...
Guiyao Ke
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On a codimension $2$ bifurcation of heteroclinic orbits [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1987 The author proves under certain conditions the existence of a heteroclinic orbit for the perturbed equation if such heteroclinic orbit exists for the unperturbed equation. From the text: We consider a bifurcation problem of heteroclinic orbits for a family of ODEs on \(\mathbb R^n\).
Hiroshi Kokubu
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Dissipation-Induced Heteroclinic Orbits in Tippe Tops [PDF]
SIAM Review, 2008 This paper demonstrates that the conditions for the existence of a dissipation-induced heteroclinic orbit between the inverted and noninverted states of a tippe top are determined by a complex version of the equations for a simple harmonic oscillator ...
Bou-Rabee, Nawaf M. +2 more
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Computing heteroclinic orbits using adjoint-based methods [PDF]
Journal of Fluid Mechanics, 2018 Transitional turbulence in shear flows is supported by a network of unstable exact invariant solutions of the Navier–Stokes equations. The network is interconnected by heteroclinic connections along which the turbulent trajectories evolve between invariant solutions.
Farano, Mirko +4 more
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Revealing asymmetric homoclinic and heteroclinic orbits
Electronic Research ArchiveAlthough scholars have proven the existence of a pair of homoclinic orbits to the origin, or a pair of heteroclinic orbits to the origin along with a pair of nontrivial equilibria in symmetric Lorenz, Chen, and Lü systems, they have rarely dealt with asymmetric ones of the corresponding asymmetric analogues, to the best of our knowledge.
Jun Pan, Haijun Wang, Feiyu Hu
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