On periodic orbits of stable flows
نویسندگان
چکیده
منابع مشابه
Periodic Orbits of Weakly Exact Magnetic Flows
For a weakly exact magnetic flows with a bounded primitive on a closed Riemannian manifold, we prove the existence of periodic orbits in almost all energy levels below of the Mañé’s critical value. Mathematics Subject Classification: 37J45
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[14]. More precisely, we have this error term if we can choose three closed orbits of least periods l1, l2, l3 such that θ = (l1 − l2)/(l2 − l3) is diophantine, i.e., there exists C > 0 and β > 0 such that |qθ − p| ≥ Cq−(1+β) for all p ∈ Z and q ∈ N. In this paper we shall consider compact groups extensions of hyperbolic flows. Let G be a compact Lie group. Let φ̂t : Λ̂ → Λ̂ be a topologically wea...
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Indeed, Margulis [lo] announced that for the geodesic flow on a d-dimensional compact manifold of curvature 1 the number of periodic orbits 7 with (minimal) period r(1) I x is asymptotic to ecd-‘jx/(d 1)x. This result bears a striking resemblance to the prime number theorem. Parry and Pollicott [12], following earlier work by Bowen [2, 41, generalized Margulis’ theorem to weakly mixing Axiom A ...
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For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bott-nondegenerate symplectic extremum of the Hamiltonian. As a consequence, we show that a charge on a compact manifold with a nondegenerate (i.e. symplectic) magnetic field has periodic orbits on a sequence of energy levels converging to zero.
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The dynamical theory of moderate Reynolds number turbulence triangulates the infinite-dimensional Navier-Stokes state space by sets of exact solutions (equilibria, relative equilibria, periodic orbits, ...) which form a rigid backbone which enables us to describe and predict the sinuous motions of a turbulent fluid. We report determination of a set of unstable periodic orbits from close recurre...
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ژورنال
عنوان ژورنال: Hokkaido Mathematical Journal
سال: 1972
ISSN: 0385-4035
DOI: 10.14492/hokmj/1535508577