Results 141 to 144 of about 7,371 (144)

Homoclinic bifurcation at resonant eigenvalues

Journal of Dynamics and Differential Equations, 1990
We consider a bifurcation of homoclinic orbits, which is an analogue of period doubling in the limit of infinite period. This bifurcation can occur in generic two parameter vector fields when a homoclinic orbit is attached to a stationary point with resonant eigenvalues.
Bo Deng, Bernold Fiedler, Shui-Nee Chow
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COMPLEXITY OF HOMOCLINIC BIFURCATIONS AND Ω-MODULI

International Journal of Bifurcation and Chaos, 1996
Bifurcations of two-dimensional diffeomorphisms with a homoclinic tangency are studied in one-and two-parameter families. Due to the well-known impossibility of a complete study of such bifurcations, the problem is restricted to the study of the bifurcations of the so-called low-round periodic orbits.
Sergey Gonchenko, Dmitry Turaev, O. V. Sten’Kin   +2 more
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Problems in homoclinic bifurcation with higher dimensions [PDF]

Acta Mathematica Sinica, 1998
Summary: A suitable local coordinate system is constructed by using exponential dichotomies and generalizing the Floquet method from periodic systems to nonperiodic systems. Then the Poincaré map is established to solve various problems in homoclinic bifurcation with codimension one or two. Bifurcation diagrams and bifurcation curves are given.
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Homoclinic loop bifurcations on a Möbius band

Nonlinearity, 1999
The author presents 1-homoclinic loop bifurcations on a non-orientable 2-manifold, the Möbius band. The techniques for studying bifurcating dynamics of the 1-homoclinic loop on this manifold are similar to those for a figure-eight loop in the plane. The key element is blow up.
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