Related papers: A Transversal for horocycle flow on H(2)
We describe all possible topological structures of Morse flows and typical gradient saddle-nod bifurcation of flows on the 2-dimensional torus with a hole in the case that the number of singular point of flows is at most six. To describe…
We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a binary grating profile together with the refractive index beneath it can be uniquely…
In this paper we consider the normal map of a closed plane curve as a vector field on the cylinder. We interpret the critical points geometrically and study their Poincar\'{e} index, including the points at infinity. After projecting the…
We show that the horocyclic flow of an orientable compact higher genus surface without conjugate points and with continuous Green bundles is uniquely ergodic. The result applies to nonflat nonpositively curved surfaces and generalizes a…
We consider the horocyclic flow corresponding to a (topologically mixing) Anosov flow or diffeomorphism, and establish the uniqueness of transverse quasi-invariant measures with H\"older Jacobians. In the same setting, we give a precise…
There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere.…
The topological dynamics of the horocyclic flow h_R on the unit tangent bundle of a geometrically finite hyperbolic surface is well known. In particular on such a surface the flow h_R is minimal or the minimal sets are the periodic orbits.…
We discuss various bifurcation problems in which two isolated periodic orbits exchange periodic ``bridge'' orbit(s) between two successive bifurcations. We propose normal forms which locally describe the corresponding fixed point scenarios…
The polarization matrix ($2\times2$) obtained from two component eigen-spinors of spherical harmonics help us to evaluate the differential matrix $N$ of the anisotropic optical medium. The geometric phase is realized through {\it helicity}…
We prove a Poincare lemma for a set of r smooth functions on a 2n-dimensional smooth manifold satisfying a commutation relation determined by r singular vector fields associated to a Cartan subalgebra of $\frak{sp}(2r,\mathbb R)$. This…
We develop a helioseismic inversion algorithm that can be used to recover sub-surface vertical profiles of 2-dimensional supergranular flows from surface measurements of synthetic wave travel times. We carry out seismic wave-propagation…
We study geodesics on hypersurfaces close to the standard (n-1)-dimensional sphere in n-dimensional Euclidean space. Following Poincar\'e, we treat the problem within the framework of the analytical mechanics, and employ the perturbation…
The paper is devoted to generic translation flows corresponding to Abelian differentials on flat surfaces of arbitrary genus $g\ge 2$. These flows are weakly mixing by the Avila-Forni theorem. In genus 2, the H\"older property for the…
We study a volume/area preserving curvature flow of hypersurfaces that are convex by horospheres in the hyperbolic space, with velocity given by a generic positive, increasing function of the mean curvature, not necessarly homogeneous. For…
In this note, we want to establish several formulas about functionals along harmonic Ricci flow on surface with boundary
We provide the first experimental demonstration of geometric phase generated in association with closed Poincar\'e Sphere trajectories comprised of geodesic arcs that do not start, end, or necessarily even include, the north and south poles…
This paper deals with fundamental properties of Poincar\'e half-maps defined on a straight line for planar linear systems. Concretely, we focus on the analyticity of the Poincar\'e half-maps, their series expansions (Taylor and…
We perform a two-dimensional inversion of f-mode travel times to determine near-surface solar flows. The inversion is based on optimally localized averaging of travel times. We use finite-wavelength travel-time sensitivity functions and a…
We analyze the geometrical structure of the passage times in the last passage percolation model. Viewing the passage time as a piecewise linear function of the weights we determine the domains of the various pieces, which are the subsets of…
We study the subsequential convergence of singular solutions to the Ricci flow with prescribed constant in space geodesic curvature on compact surfaces with boundary. Furthermore, we show that in the particular case of rotational symmetry,…