Related papers: Geodesic flows modeled by expansive flows: Compact…

In this paper, we study the quantitative recurrence properties in the case of $\mathbb{Z}$-extension of Axiom A flows on a Riemannian manifold. We study the asymptotic behavior of the first return time to a small neighborhood of the…

Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding existing spatial…

We study the geodesics on an invariant surface of a three dimensional Riemannian manifold. The main results are: the characterization of geodesic orbits; a Clairaut's relation and its geometric interpretation in some remarkable three…

Any closed, oriented, hyperbolic three-manifold with nontrivial second homology has many quasigeodesic flows, where quasigeodesic means that flow lines are uniformly efficient in measuring distance in relative homotopy classes. The flows…

For $\mathcal{O}$ a hyperbolic orientable 2-orbifold of genus $g$ with at most $2g+6$ conic points, we prove that the geodesic flow on the unitary tangent bundle$\mathrm{T}^1\mathcal{O}$ admits a Birkhoff section whose genus is one.…

In this article we prove that the Hausdorff dimension of geodesic directions that are recurrent and diverge on average coincides with the entropy at infinity of the geodesic flow for any complete, pinched negatively curved Riemannian…

Let $X$ be a compact, geodesically complete, locally CAT(0) space such that the universal cover admits a rank one axis. We prove the Bowen-Margulis measure on the space of geodesics is the unique measure of maximal entropy for the geodesic…

Motivated by numerical schemes for large scale geophysical flow, we consider the rotating shallow water and Boussinesq equations on the whole space with horizontal kinetic energy backscatter source terms built from negative viscosity and…

In this paper, we clarify the strong relationship between Myrberg type dynamics and the ergodic properties of the geodesic flows on (not necessarily compact) uniform visibility manifolds without conjugate points. We prove that the…

We construct $C^{\infty}$ time-periodic fluctuating surfaces in $\mathbb{R}^3$ such that the corresponding nonautonomous geodesic flow has orbits along which the energy, and thus the speed, goes to infinity.

We consider magnetic flows on compact quotients of the 3-dimensional solvable geometry Sol determined by the usual left-invariant metric and the distinguished monopole. We show that these flows have positive Liouville entropy and therefore…

Magnetic geodesics describe the trajectory of a particle in a Riemannian manifold under the influence of an external magnetic field. In this article, we use the heat flow method to derive existence results for such curves. We first…

We extend the concept of expansive measure \cite{am} defined for homeomorphism to flows. We obtain some properties for such measures including abscense of singularities in the support, aperiodicity, expansivity with respect to time-$T$…

We present a theory to quantify the formation of spatiotemporal macrostructures (or the non-homogeneous regions of high viscosity at moderate to high fluid inertia) for viscoelastic sub-diffusive flows, by introducing a mathematically…

We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for…

Consider the geodesic flow on a real-analytic closed hypersurface $M$ of $\mathbb{R}^n$, equipped with the standard Euclidean metric. The flow is entirely determined by the manifold and the Riemannian metric. Typically, geodesic flows are…

The geometric quantization of the geodesic flow on a compact Riemannian manifold via the BKS "dragging projection" yields the Laplacian plus a scalar curvature term. To avoid convergence issues, the standard construction involves somewhat…

In this article, we characterize two kinds of exceptional orbits of the geodesic flow associated with the Modular surface in terms of a two-parameter family of continued fraction expansion of endpoints of the lifts to the hyperbolic plane…

We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not carry full pressure. In dimension 2, this proves uniqueness for scalar…

In this paper we construct a new class of surfaces whose geodesic flow is integrable (in the sense of Liouville). We do so by generalizing the notion of tubes about curves to 3-dimensional manifolds, and using Jacobi fields we derive…