Results 221 to 230 of about 10,534 (236)

Homoclinic orbits to parabolic points

Nonlinear Differential Equations and Applications, 1997
This paper concerns non-Hamiltonian perturbations of Hamiltonian systems. Using Poincaré-Melnikov method, orbits which are homoclinic to degenerate periodic orbits of parabolic type are studied, specially the existence of transversal homoclinic points. The method used in this paper is related to a work of \textit{E.
Casasayas, Josefina, Fontich, Ernest, Nunes, Ana   +2 more
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Periodic Orbits Near Homoclinic Orbits

1982
It is known that the orbit-structure of a dynamical system near a homoclinic orbit γ is extremely complicated. However, it is only recently that this complicated structure has begun to be understood. It has been shown (under some hypotheses) that, near γ there are infinitely many long periodic orbits. The flow, near γ, admits a singular Poincare map o:
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The Dynamical Core of a Homoclinic Orbit

Regular and Chaotic Dynamics, 2022
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Hyperbolicity and the Creation of Homoclinic Orbits

The Annals of Mathematics, 1987
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Palis, J., Takens, F.
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Infinity of minimal homoclinic orbits

Nonlinearity, 2011
The 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, 2002
The 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., Bountis, T., Vrahatis, M. N.   +2 more
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NUMERICAL COMPUTATION OF HOMOCLINIC ORBITS FOR FLOWS

International Journal of Bifurcation and Chaos, 2000
It 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, 1988
A 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, 2008
The 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, 1978
We 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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