The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds

Ruelle Zeta Function at Zero for Surfaces

We show that the Ruelle zeta function for a negatively curved oriented surface vanishes at zero to the order given by the absolute value of the Euler characteristic. This result was previously known only in constant curvature.

Ruelle zeta function and Prime geodesic theorem for hyperbolic manifolds with cusps

For a d-dimensional real hyperbolic manifold with cusps, we obtain more refined error terms in the prime geodesic theorem (PGT) using the Ruelle zeta function instead of the Selberg zeta function. To do this, we prove that the Ruelle zeta function over this type manifold is a meromorphic function of order d over C.

Sinai Billiards, Ruelle Zeta-functions and Ruelle Resonances: Microwave Experiments

We discuss the impact of recent developments in the theory of chaotic dynamical systems, particularly the results of Sinai and Ruelle, on microwave experiments designed to study quantum chaos. The properties of closed Sinai billiard microwave cavities are discussed in terms of universal predictions from random matrix theory, as well as periodic orbit contributions which manifest as ‘‘scars’’ in...

Geometric models for hyperbolic 3-manifolds

In [Mi4,BrocCM1], Minsky, Brock and Canary gave a proof of Thurston’s Ending Lamination Conjecture for indecomposable hyperbolic 3-manifolds. In this paper, we offer another approach to this which was inspired by the original. Many of the key results are similar, though the overall logic is somewhat different. A possible advantage is that much of the relevant theory of “hierarchies” and other, ...

Horocycles in hyperbolic 3-manifolds