Related papers: Cusp excursions for the earthquake flow on the onc…
In a previous paper, the authors extended Mirzakhani's (almost-everywhere defined) measurable conjugacy between the earthquake and horocycle flows to a measurable bijection. In this one, we analyze the continuity properties of this map and…
The Teichmuller unipotent flow can be defined concretely on certain moduli spaces of singular flat surfaces by shearing polygonal presentations of the surfaces. Thurston's earthquake flow on moduli spaces of hyperbolic surfaces is more…
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…
We extend Mirzakhani's conjugacy between the earthquake and horocycle flows to a bijection, demonstrating conjugacies between these flows on all strata and exhibiting an abundance of new ergodic measures for the earthquake flow. The…
We track the trajectories of individual horocycles on the modular surface. Our tracking is constructive, and we thus \emph{effectively} establish topological transitivity and even line-transitivity for the horocyclic flow. We also describe…
Let $\cT$ be Teichm\"uller space of a closed surface of genus at least 2. For any point $c\in \cT$, we describe an action of the circle on $\cT\times \cT$, which limits to the earthquake flow when one of the parameters goes to a measured…
Earthquakes are rupture-like processes that propagate along tectonic faults and cause seismic waves. The propagation speed and final area of the rupture, which determine an earthquake's potential impact, are directly related to the nature…
The concept of proper time, which is different from universal time, has been introduced into the physics of earthquakes. The global activity of strong earthquakes was chosen as the object of study. We consider the sequence of earthquakes as…
For a fixed cusp neighborhood (determined by depth D) of the modular surface, we investigate the class of reciprocal geodesics that enter this neighborhood (called a cusp excursion) a fixed number of times.
We exhibit orbits of the geodesic flow on a hyperbolic surface with at least one cusp such that every tubular neighborhood contains uncountably many distinct geodesic flow orbits. The proof relies on new phenomena, namely the existence of…
Scaling analysis reveals striking regularities in earthquake occurrence. The time between any one earthquake and that following it is random, but it is described by the same universal-probability distribution for any spatial region and…
This paper endeavors to track the trajectories of individual horocycles on \modsurf. It is far more common to study \emph{sets} of such trajectories, seeking some asymptotic behavior using an averaging process (see section \ref{previous}).…
We construct a Poincar\'e section for the horocycle flow on the modular surface $SL(2, \R)/SL(2, \Z)$, and study the associated first return map, which coincides with a transformation (the {\it BCZ map}) defined by Boca-Cobeli-Zaharescu. We…
The small-scale statistical properties of velocity circulation in classical homogeneous and isotropic turbulent flows are assessed through a modeling framework that brings together the multiplicative cascade and the structural descriptions…
We investigate the sequence of great earthquakes over the past century. To examine whether the earthquake record includes temporal clustering, we identify aftershocks and remove those from the record. We focus on the recurrence time,…
Spatiotemporal clustering of earthquake events is a generally-established fact, and is important for designing models and assessment techniques in seismicity. Here, we investigate how this behavior can manifest in the statistical…
The final size of an earthquake typically cannot be predicted from its ongoing seismic radiation. Expanding observations reveal distinct exceptions, such as slow earthquakes, injection-induced seismicity, and earthquake swarms, in which…
We compute the average shape of trajectories of some one--dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between two successive returns to a reference value, finding that it obeys a scaling form. For…
We prove that the earthquake flow is at most polynomially mixing with a degree bounded by a constant depending only on the topology of the surface. In particular it is not exponentially mixing.
We report on a novel stochastic analysis of seismic time series for the Earth's vertical velocity, by using methods originally developed for complex hierarchical systems, and in particular for turbulent flows. Analysis of the fluctuations…