Related papers: Recurrence rates for observations of flows

We introduce a new object, the dynamical torsion, which extends the potentially ill-defined value at $0$ of the Ruelle zeta function of a contact Anosov flow twisted by an acyclic representation of the fundamental group. We show important…

We discuss selected topics of current research interest in the theory of dynamical systems, with emphasis on dimension theory, multifractal analysis, and quantitative recurrence. The topics include the quantitative versus the qualitative…

We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…

We consider families of diffeomorphisms with dominated splittings and preserving a Borel probability measure, and we study the regularity of the Lyapunov exponents associated to the invariant bundles with respect to the parameter. We obtain…

Aghannan and Rouchon proposed a new design method of asymptotic observers for a class of nonlinear mechanical systems: Lagrangian systems with configuration (position) measurements. The observer is based on the Riemannian structure of the…

We study the shear-induced diffusion effect and the transition to irreversibility in suspensions under oscillatory shear flow by performing an analysis of the entropy production associated to the motion of the particles. We show that the…

Any smooth surface in R^3 may be flattened along the z-axis, and the flattened surface becomes close to a billiard table in R^2 . We show that, under some hypotheses, the geodesic flow of this surface converges locally uniformly to the…

The rotational dynamics of anisotropic particles advected in a turbulent fluid flow are important in many industrial and natural setting. Particle rotations are controlled by small scale properties of turbulence that are nearly universal,…

The paper is devoted to the study of topological properties, structure and classification of Morse flows with fixed points on the boundary of three-dimensional manifolds. We construct a complete topological invariant of a Morse flow,…

We give examples of rank one compact surfaces on which there exist recurrent geodesics that cannot be shadowed by periodic geodesics. We build rank one compact surfaces such that ergodic measures on the unit tangent bundle of the surface…

We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to…

We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…

Studies of the relation between the shear parameter S^* and the Reynolds number Re are presented for a nearly homogeneous and statistically stationary turbulent shear flow. The parametric investigations are in line with a generalized…

We consider the geodesic flow of a compact connected rank 1 surface. We prove a formula for the topological pressure as the exponential growth rate of rank 1 periodic geodesics generalizing a previous result of K. Gelfert and B. Schapira…

Various notions of "zooming in" on measures exist in the literature and the scenery flow is one of them. It is of interest to describe the joint asymptotics of the scenery flows generated by a measure and the measure transported by a local…

This paper is a review on recently found connection between geodesically equivalent metrics and integrable geodesic flows. Suppose two different metrics on one manifold have the same geodesics. We show that then the geodesic flows of these…

We consider Anosov flows on closed 3-manifolds preserving a volume form $\Omega$. Following Dyatlov and Zworski (2017) we study spaces of invariant distributions with values in the bundle of exterior forms whose wavefront set is contained…

Stationary flows of an inviscid and incompressible fluid of constant density in the region $D=(0, L)\times \mathbb R^2$, periodic in the second and third variables, are considered. The flux and the Bernoulli function are prescribed at each…

Many natural real-valued functions of closed curves are known to extend continuously to the larger space of geodesic currents. For instance, the extension of length with respect to a fixed hyperbolic metric was a motivating example for the…

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…