Error Terms for Closed Orbits of Hyperbolic Flows
نویسنده
چکیده
i.e. limT→+∞ π(T ) ehT /hT = 1. This generalized a result of Margulis for geodesic flows over manifolds of negative sectional curvature [6]. It is an interesting problem to estimate the error terms in such asymptotic formulae. In the particular case of geodesic flows over compact negatively curved manifolds we showed that there was an exponential error term (with a suitable principal term) [10]. Our first result gives an error term in the case of weak-mixing transitive Anosov flows, in which case Λ =M .
منابع مشابه
Asymptotic expansion for closed orbits in homology classes for Anosov flows
In this paper we give an asymptotic expansion including error terms for the number of closed orbits in the homology classes for homological full Anosov flows. In particular we obtain formulae concerning the coefficients of error terms which depend on the homology classes.
متن کاملCoarse Hyperbolicity and Closed Orbits for Quasigeodesic Flows
We prove Calegari’s conjecture that every quasigeodesic flow on a closed hyperbolic 3-manifold has closed orbits.
متن کاملOrbit Spaces Arising from Isometric Actions on Hyperbolic Spaces
Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology. Dimension of is called the cohomogeneity of the action of on . If is a differentiable manifold of cohomogeneity one under the action of a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...
متن کاملPeriodic Orbits and Holonomy for Hyperbolic Flows
[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...
متن کاملFuzzy Sliding Mode for Spacecraft Formation Control in Eccentric Orbits
The problem of relative motion control for spacecraft formation flying in eccentric orbits is considered in this paper. Due to the presence of nonlinear dynamics and external disturbances, a robust fuzzy sliding mode controller is developed. The slopes of sliding surfaces of the conventional sliding mode controller are tuned according to error states using a fuzzy logic and reach the pre-define...
متن کامل