Related papers: Earthquakes on the once-punctured torus
An attempt to construct a phenomenological theory of earthquakes is being undertaken by a small research team, which includes the author. We have only taken the first steps towards goal, but the results already obtained convincingly…
In considering the mathematical problem of describing the geodesics on a torus or any other surface of revolution, there is a tremendous advantage in conceptual understanding that derives from taking the point of view of a physicist by…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
We consider circle patterns on closed tori equipped with complex projective structures. There is an embedding of the space of circle patterns to the Teichm\"{u}ller space of a punctured surface. Via the embedding, the Weil-Petersson…
A two-dimensional earthquake model that consists of a single block resting upon a slowly moving rough surface and connected by two springs to rigid supports is studied. Depending on the elastic anisotropy and the friction force three…
Various problems of geometry, topology and dynamical systems on surfaces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a flat metric with several cone-type…
Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The…
We discuss various methods used to investigate the geometric complexity of earthquakes and earthquake faults, based both on a point-source representation and the study of interrelations between earthquake focal mechanisms. We briefly review…
We show that Thurston's earthquake flow is strongly asymmetric in the sense that its normalizer is as small as possible inside the group of orbifold automorphisms of the bundle of measured geodesic laminations over moduli space. (At the…
A well-known theorem of Wolpert shows that the Weil-Petersson symplectic form on Teichm\"uller space, computed on two infinitesimal twists along simple closed geodesics on a fixed hyperbolic surface, equals the sum of the cosines of the…
We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of…
Thurston's earthquake theorem asserts that every orientation-preserving homeomorphism of the circle admits an extension to the hyperbolic plane which is a (left or right) earthquake. The purpose of these notes is to provide a proof of…
In this paper, we apply techniques of geometric quantization to study the response of the integer and fractional quantum Hall effects to toroidal geometry deformation. The main method is that of using complex time Hamiltonian evolution to…
This paper combines the power of deep-learning with the generalizability of physics-based features, to present an advanced method for seismic discrimination between earthquakes and explosions. The proposed method contains two branches: a…
In this paper we will use b-groups to construct coordinates for the Teichm\"uller spaces of 2-orbifolds. The main technical tool is the parametrization of triangle groups, which allows us to compute explicitly formul\ae\ for generators of…
We consider deformations of a group of circle diffeomorphisms with H\"older continuous derivatives in the framework of quasiconformal Teichm\"uller theory and show certain rigidity under conjugation by symmetric homeomorphisms of the…
We show that the action of the mapping class group on the space of closed curves of a closed surface effectively tracks the corresponding action on Teichm\"uller space in the following sense: for all but quantitatively few mapping classes,…
We construct new coordinates for the Teichm\"uller space Teich of a punctured torus into $\bold{R} \times\bold{R}^+$. The coordinates depend on the representation of Teich as a space of marked Kleinian groups $G_\mu$ that depend…
We study the coarse geometry of the moduli space of dilation tori with two singularities and the dynamical properties of the action of the Teichmuller flow on this moduli space. This leads to a proof that the vertical foliation of a…
We study the deformation theory of nonsigular projective curves defined over algebraic closed fields of positive characteristic. We show that under some assumptions the local deformation problem for automorphisms of powerseries can be…