Related papers: Barcode entropy of geodesic flows

We consider the geodesic flow of reversible Finsler metrics on the 2-sphere and the 2-torus, whose geodesic flow has vanishing topological entropy. Following a construction of A. Katok, we discuss examples of Finsler metrics on both…

In this paper we study the behavior of geodesics on cones over arbitrary $C^3$-smooth closed Riemannian manifolds. We show that the geodesic flow on such cones admits first integrals whose values uniquely determine almost all geodesics…

In many applications, the two-dimensional trajectories of fluid particles are available, but little is known about the underlying flow. Oceanic floats are a clear example. To extract quantitative information from such data, one can measure…

On a Riemannian 2-torus $(T^2,g)$ we study the geodesic flow in the case of low complexity described by zero topological entropy. We show that this assumption implies a nearly integrable behavior. In our previous paper \cite{GK} we already…

We consider the ergodic theory of plane rational maps that preserve the natural holomorphic volume form on the algebraic torus. Specifically we construct natural invariant probability measures for a large class of such maps by intersecting…

We study a flow of $G_2$ structures which induce the same Riemannian metric which is the negative gradient flow of an energy functional. We prove Shi-type estimates for the torsion tensor along the flow. We show that at a finite-time…

We study the topological entropy of the magnetic flow on a closed riemannian surface. We prove that if the magnetic flow has a non-hyperbolic closed orbit in some energy set T^cM= E^{-1}(c), then there exists an exact $…

We prove that the geodesic flow on a locally CAT(-1) metric space which is compact, or more generally convex cocompact with non-elementary fundamental group, can be coded by a suspension flow over an irreducible shift of finite type with…

In this paper, we introduce an entropy functional on Riemannian foliation, inspired by the work of , which is monotonically along the transverse Ricci flow. We relate their gradient flow, via diffeomorphism preserving the foliated structure…

We consider a transversally conformal foliation $\mathcal{F}$ of a closed manifold $M$ endowed with a smooth Riemannian metric whose restriction to each leaf is negatively curved. We prove that it satisfies the following dichotomy. Either…

We give lower bounds for the growth of the number of Reeb chords and for the volume growth of Reeb flows on spherizations over closed manifolds M that are not of finite type, have virtually polycyclic fundamental group, and satisfy a mild…

A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…

We compute the entropy of a closed bounded region of space for pure 3d Riemannian gravity formulated as a topological BF theory for the gauge group SU(2) and show its holographic behavior. More precisely, we consider a fixed graph embedded…

In this paper, we present an algorithm for the computation of harmonic maps, and respectively, of the harmonic map heat flow between two closed Riemannian manifolds. Our approach is based on the totally geodesic embedding of the target…

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive sectional curvature. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow…

In the unit tangent bundle of noncompact finite volume negatively curved Riemannian manifolds, we prove the equidistribution towards the measure of maximal entropy for the geodesic flow of the Lebesgue measure along the divergent geodesic…

We employ the curve shortening flow to establish three new results on the dynamics of geodesic flows of closed Riemannian surfaces. The first one is the stability, under $C^0$-small perturbations of the Riemannian metric, of certain flat…

We establish a precise asymptotic formula for the number of homotopy classes of periodic orbits for the geodesic flow on rank one manifolds of nonpositive curvature. This extends a celebrated result of G. A. Margulis to the nonuniformly…

We study the entropy of Sinai-Ruelle-Bowen measure of the geodesic flow on convex real projective surfaces, and shows that the Hilbert area tends to infinity if the entropy tends to zero. For the Blaschke metric, the area tends to infinity…

Motivated by a paper of Bolsinov and Taimanov DG/9911193 we consider non-holonomic situation and exhibit examples of sub-Riemannian metrics with integrable geodesic flows and positive topological entropy. Moreover the Riemannian examples…