Notes on thermodynamic formalism for Anosov flows
Symbolic dynamics and geodesic flows
Factorisation of Lefschetz zeta functions and twisted periodic orbits.
Large deviations, Gibbs measures and closed orbits for hyperbolic flows.
On the rate of mixing of Axiom A flows.
Distributions at infinity for Riemann surfaces
Distribution of closed geodesics on the modular surface and quadratic irrationals
Normal points for generic hyperbolic maps
We consider families of hyperbolic maps and describe conditions for a fixed reference point to have its orbit evenly distributed for maps corresponding to generic parameter values.
The Circle Problem on Surfaces of Variable Negative Curvature.
Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature.
Linear actions of free groups
In this paper we study dynamical properties of linear actions by free groups via the induced action on projective space. This point of view allows us to introduce techniques from Thermodynamic Formalism. In particular, we obtain estimates on the growth of orbits and their limiting distribution on projective space.
Unique Bernoulli -measures
We improve and subsume the conditions of Johansson and Öberg and Berbee for uniqueness of a -measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique -measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the -measure.
A note on the asymptotics of perturbed expanding maps.
A thermodynamic approach to locally symmetric manifolds of higher rank
Sets of nondifferentiability for conjugacies between expanding interval maps
We study differentiability of topological conjugacies between expanding piecewise interval maps. If these conjugacies are not C¹, then their derivative vanishes Lebesgue almost everywhere. We show that in this case the Hausdorff dimension of the set of points for which the derivative of the conjugacy does not exist lies strictly between zero and one. Moreover, by employing the thermodynamic formalism, we show that this Hausdorff dimension can be determined explicitly in terms of the Lyapunov spectrum....
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