Results 131 to 140 of about 646 (172)

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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Poincar�'s discovery of homoclinic points

Archive for History of Exact Sciences, 1994
The author claims that the most radical break with prevailing conceptions was Poincaré's discovery of homoclinic points, which nowadays figure in studies of ``chaotic'' motions. The presence of a homoclinic point in a dynamical system complicates the orbit structure considerably and implies the existence of trajectories with quite unpredictable ...
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The homoclinic twist bifurcation point

1992
We analyze bifurcations occurring in the vicinity of a homoclinic twist point for a generic two parameter family of Z 2 equivariant ODE’s in four dimensions. The results are compared with numerical results for a system of two coupled Josephson junctions with pure capacitive load.
Aronson, D.G., van Gils, S.A., Krupa, M.
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Homoclinic points in higher dimensional dynamical systems

Physica Scripta, 1991
A Melnikov type condition for the existence of homoclinic points in higher dimensional dynamical systems is discussed. An application to the homoclinic bifurcations in a parametrically driven Lorenz system is described. For selected parameters the theoretical predictions are checked by numerical experiments.
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Homoclinic points of non-expansive automorphisms

Aequationes mathematicae, 2008
We study homoclinic points of non-expansive automorphisms of compact abelian groups. Connections between the existence of non-trivial homoclinic points, expansiveness, entropy and adjoint automorphisms (in the sense of Einsiedler and Schmidt) are explored.
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Homoclinic Points of Principal Algebraic Actions

2016
The 1999 paper by D. Lind and K. Schmidt on homoclinic points of a special class of dynamical systems—the so called algebraic \({{\mathrm{\mathbb {Z}^d}}}\)-actions—attracted a lot of interest to the study of homoclinic points. In the present paper we review the developments over the past 15 years. Major progress has been made in questions of existence
Martin Göll, Evgeny Verbitskiy
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Numerical Computation of Saddle-Node Homoclinic Bifurcation Points

SIAM Journal on Numerical Analysis, 1993
This paper presents the convergence and stability of a numerical method for computing the intersection points of homoclinic bifurcation curves and saddle-node or transcritical bifurcation curves.
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Universal pattern for homoclinic and periodic points

Physica D: Nonlinear Phenomena, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bevilaqua, D. V., de Matos, M. Basílio
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Three-Body Problem, Poincaré Recurrence, Homoclinic Points

2014
In this session we will change the subject and come back to more fundamental questions in physics. The main subject I propose to talk about is the many body problem. As a first step, let me ask you; what is a two-body system? What are the special points?
Ali Sanayei, Otto E. Rössler
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Three dimensional expansive diffeomorphisms with homoclinic points

Boletim da Sociedade Brasileira de Matem�tica, 1996
Let \(M\) be a compact connected oriented three-dimensional manifold and let \(f:M \to M\) be an expansive diffeomorphism such that \(\Omega (f)=M\). The author proves that if there exists a hyperbolic periodic point with a homoclinic intersection then \(f\) is conjugate to an Anosov isomorphism of \(T^3\).
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