scholarly journals Ergodicity of the Geodesic Flow on Non-complete Negatively Curved Surfaces

2009 ◽  
Vol 13 (3) ◽  
pp. 405-420 ◽  
Author(s):  
Mark Pollicott ◽  
Howie Weiss
Keyword(s):  
Geodesic Flow ◽  
Curved Surfaces ◽  
Negatively Curved

scholarly journals A Lower Bound for the Remainder in Weyl's Law on Negatively Curved Surfaces

2007 ◽  
Vol 2007 ◽  
Author(s):  
Dmitry Jakobson ◽  
Iosif Polterovich ◽  
John A. Toth
Keyword(s):  
Lower Bound ◽  
Curved Surfaces ◽  
Weyl’S Law ◽  
Negatively Curved ◽  
Weyl's Law

scholarly journals Number of nodal domains and singular points of eigenfunctions of negatively curved surfaces with an isometric involution

2016 ◽  
Vol 102 (1) ◽  
pp. 37-66 ◽  
Author(s):  
Junehyuk Jung ◽  
Steve Zelditch
Keyword(s):  
Singular Points ◽  
Curved Surfaces ◽  
Nodal Domains ◽  
Negatively Curved

scholarly journals Gibbs measures for foliated bundles with negatively curved leaves

2016 ◽  
Vol 38 (4) ◽  
pp. 1238-1288 ◽  
Author(s):  
SÉBASTIEN ALVAREZ
Keyword(s):  
Invariant Measure ◽  
Gibbs Measure ◽  
Geodesic Flow ◽  
Gibbs Measures ◽  
Holonomy Group ◽  
Bijective Correspondence ◽  
Weighted Averages ◽  
Negatively Curved ◽  
Harmonic Measures ◽  
Foliated Bundle

In this paper we develop a notion of Gibbs measure for the geodesic flow tangent to a foliated bundle over a compact negatively curved base. We also develop a notion of$F$-harmonic measure and prove that there exists a natural bijective correspondence between these two concepts. For projective foliated bundles with$\mathbb{C}\mathbb{P}^{1}$-fibers without transverse invariant measure, we show the uniqueness of these measures for any Hölder potential on the base. In that case we also prove that$F$-harmonic measures are realized as weighted limits of large balls tangent to the leaves and that their conditional measures on the fibers are limits of weighted averages on the orbits of the holonomy group.

scholarly journals Approximate solutions of cohomological equations associated with some Anosov flows

1990 ◽  
Vol 10 (2) ◽  
pp. 367-379 ◽  
Author(s):  
Svetlana Katok
Keyword(s):  
Approximate Solutions ◽  
Geodesic Flows ◽  
Curved Surfaces ◽  
Anosov Flow ◽  
3 Dimensional ◽  
Negatively Curved ◽  
Anosov Flows ◽  
Higher Differentiability ◽  
Special Case ◽  
Cohomological Equations

AbstractThe Livshitz theorem reported in 1971 asserts that any C1 function having zero integrals over all periodic orbits of a topologically transitive Anosov flow is a derivative of another C1 function in the direction of the flow. Similar results for functions of higher differentiability have also appeared since. In this paper we prove a ‘finite version’ of the Livshitz theorem for a certain class of Anosov flows on 3-dimensional manifolds which include geodesic flows on negatively curved surfaces as a special case.

scholarly journals Dynamics of the geodesic flow of a foliation

1988 ◽  
Vol 8 (4) ◽  
pp. 637-650 ◽  
Author(s):  
Paweł G. Walczak
Keyword(s):  
Riemannian Manifold ◽  
Lyapunov Exponents ◽  
Geodesic Flow ◽  
Smooth Measure ◽  
Curved Manifolds ◽  
Negatively Curved ◽  
Foliated Riemannian Manifold

AbstractThe geodesic flow of a foliated Riemannian manifold (M, F) is studied. The invariance of some smooth measure is established under some geometrical conditions on F. The Lyapunov exponents and the entropy of this flow are estimated. As an application, the non-existence of foliations with ‘short’ second fundamental tensors is obtained on compact negatively curved manifolds.

scholarly journals Harmonic measures and the foliated geodesic flow for foliations with negatively curved leaves

2014 ◽  
Vol 36 (2) ◽  
pp. 355-374 ◽  
Author(s):  
SÉBASTIEN ALVAREZ
Keyword(s):  
Gibbs Measure ◽  
Geodesic Flow ◽  
Bijective Correspondence ◽  
Negatively Curved ◽  
Harmonic Measures

In this paper we define a notion of Gibbs measure for the geodesic flow tangent to a foliation with negatively curved leaves and associated to a particular potential $H$. We prove that there is a canonical bijective correspondence between these measures and Garnett’s harmonic measures.

scholarly journals Local geometry of random geodesics on negatively curved surfaces

2021 ◽  
Vol 4 ◽  
pp. 187-226
Author(s):  
Jayadev Athreya ◽  
Steve Lalley ◽  
Jenya Sapir ◽  
Matthew Wroten
Keyword(s):  
Local Geometry ◽  
Curved Surfaces ◽  
Negatively Curved

scholarly journals Survival of short-range order in the Ising model on negatively curved surfaces

2009 ◽  
Vol 80 (2) ◽  
Author(s):  
Yasunori Sakaniwa ◽  
Hiroyuki Shima
Keyword(s):  
Ising Model ◽  
Short Range ◽  
Short Range Order ◽  
Range Order ◽  
Curved Surfaces ◽  
Negatively Curved
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