Results 181 to 190 of about 9,394 (211)
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Hyperbolicity and the Creation of Homoclinic Orbits
The Annals of Mathematics, 1987zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Palis, J., Takens, F.
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Infinity of minimal homoclinic orbits
Nonlinearity, 2011The existence of homoclinic orbits for positive definite Lagrangians to hyperbolic tori (or Aubrey sets) has been proved by many authors. In this paper the author considers Lagrangian functions \(L\in C^2(TM\times \mathbb{R}, \mathbb{R})\) that are positive definite, have superlinear growth, are complete and \(1\)-periodic in the real factor.
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Homoclinic orbits of invertible maps
Nonlinearity, 2002The authors describe two methods of approximation of homoclinic trajectories of a saddle fixed point for a discrete dynamical system. Both methods are based on reduction of the problem to the search for homoclinic trajectories with special symmetries for some systems of higher dimension. As examples, a cubic map and the Hénon map are considered.
Bergamin, J. M. +2 more
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NUMERICAL COMPUTATION OF HOMOCLINIC ORBITS FOR FLOWS
International Journal of Bifurcation and Chaos, 2000It is shown that numerical computation of homoclinic orbits for flows will generate transverse homoclinic points when one uses very accurate schemes.
Chan, Whei-Ching C., Wang, Dah-Zen
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Errata: Homoclinic Orbits in Slowly Varying Oscillators
SIAM Journal on Mathematical Analysis, 1988A small correction to ibid. 18, 612-629 (1987; Zbl 0622.34041).
Wiggins, Stephen, Holmes, Philip
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Homoclinic Orbits of Nonlinear Functional Difference Equations
Acta Applicandae Mathematicae, 2008The author employs the critical point theory to obtain the existence of a nontrivial homoclinic orbit which decays exponentially at infinity for nonlinear difference equations containing both advance and retardation without any periodic assumptions. Moreover, if the nonlinearity is an odd function, the existence of an unbounded sequence of nontrivial ...
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Transversal Homoclinic Orbits in an Integrable System
American Journal of Mathematics, 1978We construct a Hamiltonian system on TP' which admits a hyperbolic equilibrium point together with 2n transversal homoclinic orbits. However, the system is completely integrable, and hence X possesses no invariant subsystems topologically conjugate to the suspension of a Bernoulli shift.
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Generating Chaos with Saddle-Focus Homoclinic Orbit
International Journal of Bifurcation and ChaosThis paper develops an anticontrol approach to design a 3D continuous-time autonomous chaotic system with saddle-focus homoclinic orbit, based on two chaotification criterions for all orbits to be globally bounded with positive Lyapunov exponents.
Chaoxia Zhang +2 more
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