Existence of relative periodic orbits near relative equilibria
نویسندگان
چکیده
منابع مشابه
Existence of Relative Periodic Orbits near Relative Equilibria
We show existence of relative periodic orbits (a.k.a. relative nonlinear normal modes) near relative equilibria of a symmetric Hamiltonian system under an appropriate assumption on the Hessian of the Hamiltonian. This gives a relative version of the Moser-Weinstein theorem.
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We consider G-equivariant semilinear parabolic equations where G is a finite-dimensional possibly non-compact symmetry group. We treat periodic forcing of relative equilibria and resonant periodic forcing of relative periodic orbits as well as Hopf bifurcation from relative equilibria to relative periodic orbits using LyapunovSchmidt reduction. Our main interest are drift phenomena caused by re...
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We give explicit differential equations for a symmetric Hamiltonian vector field near a relative periodic orbit. These decompose the dynamics into periodically forced motion in a Poincaré section transversal to the relative periodic orbit, which in turn forces motion along the group orbit. The structure of the differential equations inherited from the symplectic structure and symmetry propertie...
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We study the bundle structure near reversible relative periodic orbits in reversible equivariant systems. In particular we show that the vector eld on the bundle forms a skew product system, by which the study of bifurcation from reversible relative periodic solutions reduces to the analysis of bifurcation from reversible discrete rotating waves. We also discuss possibilities for drifts along g...
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Relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur for example in celestial mechanices, molecular dynamics and rigid body motion. RPOs are solutions which are periodic orbits of the symmetry-reduced system. In this paper we analyze certain symmetry-breaking bifurcations of Hamiltonian relative periodic orbits and show how they can be detected and computed ...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2004
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2004.v11.n3.a11