Symbolic dynamics and geodesic flows

The Dynamics of Geodesic Flows*

Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits

0. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part I. Renewal theorems in symbolic dynamics . . . . . . . . . . . . 1. Background: Shifts, suspension flows, thermodynamic formalism . 2. 3. 4. 5. 6. 7. 1 5 5 Renewal measures and renewal theorems . . . . . . . . . . . . . . 7 A modification for finite sequences . . . . . . . . . . . . . . . . . 10 Equidistribution theo...

Symbolic Dynamics for the Geodesic Flow on Hecke Surfaces

In this paper we discuss a coding and the associated symbolic dynamics for the geodesic flow on Hecke triangle surfaces. We construct an explicit cross section for which the first return map factors through a simple (explicit) map given in terms of the generating map of a particular continued fraction expansion closely related to the Hecke triangle groups. We also obtain explicit expressions fo...

Are Hamiltonian Flows Geodesic Flows?

When a Hamiltonian system has a \Kinetic + Potential" structure, the resulting ow is locally a geodesic ow. But there may be singularities of the geodesic structure, so the local structure does not always imply that the ow is globally a geodesic ow. In order for a ow to be a geodesic ow, the underlying manifold must have the structure of a unit tangent bundle. We develop homological conditions ...

Geodesic Information Flows

Homogenising the availability of manually generated information in large databases has been a key challenge of medical imaging for many years. Due to the time consuming nature of manually segmenting, parcellating and localising landmarks in medical images, these sources of information tend to be scarce and limited to small, and sometimes morphologically similar, subsets of data. In this work we...