Related papers: Dynamics on an infinite surface with the lattice p…
Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements.…
The loop graph of an infinite type surface is an infinite diameter hyperbolic graph first studied in detail by Juliette Bavard. An important open problem in the study of infinite type surfaces is to describe the boundary of the loop graph…
We construct a smooth rational affine surface S with finite automorphism group but with the property that the group of automorphisms of the cylinder SxA^2 acts infinitely transitively on the complement of a closed subset of codimension at…
Two identical particles driven by the same steady force through a viscous fluid may move relative to one another due to hydrodynamic interactions. The presence or absence of this relative translation has a profound effect on the dynamics of…
Following recent work of T. Alazard and C. Shao on applications of para-differential calculus to smooth conjugacy and stability problems for Hamiltonian systems, we prove finite codimension stability of invariant surfaces (in finite…
We show that the isometry group of a finite-volume hyperbolic 3-manifold acts simply transitively on many of its closed geodesics. Combining this observation with the Virtual Special Theorems of the first author and Wise, we show that every…
An asymmetrical 2D Ising model with a zigzag surface, created by diagonally cutting a regular square lattice, has been developed to investigate the thermodynamics and phase transitions on surface by the methodology of recursive lattice,…
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…
We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this…
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 give strongly aperiodic subshifts of finite type on every hyperbolic surface group; more generally, for each pair of expansive primitive symbolic substitution systems with incommensurate growth rates, we construct strongly aperiodic…
In the first part of this work we explore the geometry of infinite type surfaces and the relationship between its convex core and space of ends. In particular, we show that a geodesically complete hyperbolic surface is made up of its convex…
We prove a structure theorem for ergodic homological rotation sets of homeomorphisms isotopic to the identity on a closed orientable hyperbolic surface: this set is made of a finite number of pieces that are either one-dimensional or almost…
We show the following result: If $X_0$ is an affine surface over a field $K$ and $f, g$ are two loxodromic automorphisms with an orbit meeting infinitely many times, then $f$ and $g$ must share a common iterate. The proof uses the…
We introduce and study a deterministic lattice model describing the motion of an infinite system of oppositely charged particles under the action of a constant electric field. As an application this model represents a traffic flow of cars…
The author shows that equicontinuous geodesic flows on surfaces are periodic. A similar result for flows on 3-manifolds is also proven. The idea of the proof is to show that the return map is recurrent and therefore periodic.
Discussed is a model of collective and internal degrees of freedom with kinematics based on affine group and its subgroups. The main novelty in comparison with the previous attempts of this kind is that it is not only kinematics but also…
The motion of a rigid body immersed in an incompressible perfect fluid which occupies a three- dimensional bounded domain have been recently studied under its PDE formulation. In particular classical solutions have been shown to exist…
We describe the "hyperbolic" properties of a riemann surface lamination M canonically associated to every compact three manifolds of curvature less than 1. More precisely, if the geodesic flow is the phase space attached to an ordinary…
The orbit closure of any translation surface under the horocycle flow in almost any direction equals its $SL_2(\mathbb{R})$ orbit closure. This result gives rise to new characterizations of lattice surfaces in terms of the hororcycle flow.