Hamiltonian Systems Near Relative Periodic Orbits
نویسندگان
چکیده
منابع مشابه
Hamiltonian Systems Near Relative Periodic Orbits
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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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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The bifurcation theory and numerics of periodic orbits of general dynamical systems is well developed, and in recent years there has been rapid progress in the development of a bifurcation theory for dynamical systems with structure, such as symmetry or symplecticity. But as yet there are few results on the numerical computation of those bifurcations. The methods we present in this paper are a ...
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The present paper is a review of counterexamples to the “Hamiltonian Seifert conjecture” or, more generally, of examples of Hamiltonian systems having no periodic orbits on a compact energy level. We begin with the discussion of the “classical” and volume– preserving Seifert conjectures. Then the constructions of counterexamples to the Hamiltonian Seifert conjecture in dimensions greater than o...
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ژورنال
عنوان ژورنال: SIAM Journal on Applied Dynamical Systems
سال: 2002
ISSN: 1536-0040
DOI: 10.1137/s1111111101387760