منابع مشابه
Generic Twistless Bifurcations
We show that in the neighborhood of the tripling bifurcation of a periodic orbit of a Hamiltonian flow or of a fixed point of an area preserving map, there is generically a bifurcation that creates a “twistless” torus. At this bifurcation, the twist, which is the derivative of the rotation number with respect to the action, vanishes. The twistless torus moves outward after it is created, and ev...
متن کاملThe Geometry of Generic Sliding Bifurcations
Using the singularity theory of scalar functions, we derive a classification of sliding bifurcations in piecewise-smooth flows. These are global bifurcations which occur when distinguished orbits become tangent to surfaces of discontinuity, called switching manifolds. The key idea of the paper is to attribute sliding bifurcations to singularities in the manifold’s projection along the flow, nam...
متن کاملTwistless KAM tori.
A selfcontained proof of the KAM theorem in the Thirring model is discussed. I shall particularize the Eliasson method, E], for KAM tori to a special model, of great interest, whose relevance for the KAM problem was pointed out by Thirring, T] (see G] for a short discussion of the model). The idea of exposing Eliasson's method through simple particular cases appears in V], where results of the ...
متن کاملBifurcations of Generic heteroclinic Loop Accompanied by Transcritical bifurcation
The bifurcations of generic heteroclinic loop with one nonhyperbolic equilibrium p1 and one hyperbolic saddle p2 are investigated, where p1 is assumed to undergo transcritical bifurcation. Firstly, we discuss bifurcations of heteroclinic loop when transcritical bifurcation does not happen, the persistence of heteroclinic loop, the existence of homoclinic loop connecting p1 (resp. p2) and the co...
متن کاملDetection of Generic One Parameter Bifurcations of Hamiltonian Equilibria
In this paper several possibilities are considered for constructing test functions which reveal generic one parameter bifurcations of equilibria of Hamiltonian systems. These are alternatives to computing all the eigenvalues of the linearized system. Because of the Hamiltonian structure, most test functions that are used for general systems do not work here. Typically a test function that shoul...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinearity
سال: 1999
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/13/1/310