LARGE DEVIATIONS, FLUCTUATIONS AND SHRINKING INTERVALS (2009)
Abstract. This paper concerns the statistical properties of hyperbolic diffeomorphisms. We obtain a large deviation result with respect to slowly shrinking intervals for a large class of Hölder...
LARGE DEVIATIONS FOR INTERMITTENT MAPS (2009)
Abstract. In this note we study large deviation results for the Manneville-Pomeau map and related transformations. In particular, we consider conditions under which the associated error term is...
CHEBOTAREV-TYPE THEOREMS IN HOMOLOGY CLASSES (2009)
Abstract. We describe how closed geodesics lying in a prescribed homology class on a negatively curved manifold split when lifted to a finite cover. This generalizes a result of Zelditch in the case...
PERIODIC ORBITS AND HOLONOMY FOR HYPERBOLIC FLOWS (2009)
One of the most natural problems in ergodic theory to understand the asymptotic behaviour of various orbital averages. Such an approach is particularly fruitful in the case of hyperbolic systems....
Recovering the time-dependent transmission rate from epidemiological data (2009)
Pollicott, Mark, Wang, Hao, Weiss, Howie
The transmissibility of many infectious diseases varies significantly in time, but has been thought impossible to measure directly. We devise a mathematical algorithm to recover the time-dependent...
ASYMPTOTIC EXPANSIONS FOR CLOSED ORBITS IN HOMOLOGY CLASSES (2009)
The Erwin, Schrödinger International Boltzmanngasse, Mark Pollicott, Richard Sharp, Mark Pollicott, Richard Sharp
Let V be a smooth compact manifold with first Betti number b> 0 equipped with a Riemannian metric of (possibly variable) negative curvature. Such a manifold has a countable infinity of closed...
Dedicated to Jorge Sotomayor on the occasion of his sixtieth birthday. In this note we explore how simple tools from differential geometry can be used to analyze the behavior of some solutions curves...
Sets of non-differentiability for conjugacies between expanding interval maps (2008)
Jordan, Thomas, Kesseböhmer, Marc, Pollicott, Mark, Stratmann, Bernd O.
We study differentiability of topological conjugacies between expanding piecewise $C^{1+\epsilon}$ interval maps. If these conjugacies are not $C^1$, then they have zero derivative almost everywhere....
An analogue of Bauer’s theorem for closed orbits of skew products (2008)
Parry, William, Pollicott, Mark
In this article we prove an analogue of Bauer’s theorem from algebraic number theory in the context of hyperbolic systems.
Addendum: an analogue of Artin reciprocity for closed orbits of skew products (2008)
Pollicott, Mark, Sharp, Richard
One of the unfulfilled aims of the authors of the preceding paper [W. Parry and M. Pollicott. An analogue of Bauer’s theorem for closed orbits of skew products. Ergod. Th. & Dynam. Sys. 28 (2008),...
The mathematical research of William Parry FRS (2008)
Pollicott, Mark, Sharp, R., Tuncel, S.
In this article we survey the mathematical research of the late William (Bill) Parry, FRS.
PSEUDO-ANOSOV FOLIATIONS ON PERIODIC SURFACES (2008)
In this note we shall study the lifts of stable foliations of pseudo-Anosov diffeomorphism to certain infinite abelian covers. This is motivated, at least in part, by recent progress in understanding...
Correlations for pairs of closed geodesics (2008)
Abstract. In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic estimates for pairs of closed geodesics, the differences of...
AN ANALOGUE OF BAUER’S THEOREM FOR CLOSED ORBITS OF SKEW PRODUCTS (2008)
Let φ: X → X be a hyperbolic dynamical system and, for a finite G, let �φ: � X → � X be a G-extension for which � φ is also hyperbolic. Given φ we are interested in describing the...
DISTRIBUTION OF ERGODIC SUMS FOR HYPERBOLIC MAPS (2008)
Dedicated to Anatoly Vershik on the occasion of his seventieth birthday. Abstract. In this paper we study statistical properties of hyperbolic maps. In particular, we estimate how sums of functions...
Multifractal analysis of non-uniformly hyperbolic systems (2008)
Johansson, Anders, Jordan, Thomas, Öberg, Anders, Pollicott, Mark
We prove a multifractal formalism for Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville--Pomeau map.
Ergodicity of the Geodesic Flow on Non-complete Negatively Curved Surfaces (2008)
We study the dynamics of the geodesic flow for a class of non-complete Riemannian metrics on a negatively curved surface M. These finite area surfaces are composed of finitely many “singular”...
Countable state shifts and uniqueness of g -measures (2007)
Johansson, Anders., Öberg, Anders., Pollicott, Mark.
American Journal of Mathematics - Volume 129, Number 6, December 2007
. For the Ulam-von Neumann map Tx = 4x(1 \Gamma x), (2007)
Mark Pollicott, Oliver Jenkinson
Abstract. We present a method for accurately computing the metric entropy (or, equivalently, the Lyapunov exponent) of the absolutely continuous invariant measure for a piecewise analytic expanding...
Calculating Hausdorff dimension of Julia sets and Kleinian limit sets (2007)
Oliver Jenkinson, Mark Pollicott
Abstract. We present a new algorithm for eciently computing the Hausdor dimension of sets X invariant under conformal expanding dynamical systems. By locating the periodic points of period up to N,...
Oliver Jenkinson and Mark Pollicott (2007)
Oliver Jenkinson, Mark Pollicott
. We consider the ergodic properties of the Bolyai-R'enyi expansion for real numbers introduced in [Bol], [Ren]. We compute the entropy of the absolutely continuous invariant probability measure...
Linear Actions of Free Groups (2007)
. 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...
Periodic Orbits and Zeta Functions (2007)
Introduction 1 1. Twisted orbits and zeta functions 3 2. Axiom A diffeomorphisms 4 3. Symbolic dynamics and rationality 5 4. Zeta functions and for interval maps 9 5. The Ruelle zeta function 14 6....
Livsic's Theorem for Semisimple Lie groups (2007)
Matthew Nicol Mark, Mark Pollicott
In this note we show that strong generalizations of the measurable Livsic theorem for cocycles taking values in connected noncompact linear semisimple Lie groups, a canonical example being SL(2; R),...
Dynamical Zeta Functions (2007)
a non-zero radius of convergence, and therefore converges to an analytic function for jzj sufficiently small. An important class of C 1 diffeomorphisms for which the zeta function i f (z) is better...
LARGE DEVIATIONS AND THE DISTRIBUTION OF PRE-IMAGES OF RATIONAL MAPS (2007)
Abstract. In this article we prove a large deviation result for the pre-images of a point in the Julia set of a rational mapping of the Riemann sphere. As a corollary, we deduce a convergence result...
ANGULAR SELF-INTERSECTIONS FOR CLOSED GEODESICS ON SURFACES (2007)
Abstract. In this note we consider asymptotic results for self-interections of closed geodesics on surfaces for which the angle of the intersection occurs in a given arc. We do this by extending...
POINCAR E SERIES AND ZETA FUNCTIONS FOR SURFACE GROUP ACTIONS ON R-TREES (2007)
For a discrete group of isometries \Gamma acting freely on n-dimensional hyperbolic space H
LINEAR ACTIONS OF FREE GROUPS (2007)
Abstract. 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...
Error terms for closed orbits of hyperbolic flows, Ergodic Theory Dynam (2007)
In this paper we shall consider error terms in estimates for the number of closed
GROWTH OF PERIODIC POINTS AND ROTATION VECTORS ON SURFACES (2007)
In this paper will consider diffeomorphisms f: M! M of a compact surface M, isotopic to the identity map, and study the growth of their periodic points.
Let C denote the Riemann sphere and let T: (2007)
Abstract. In this article we prove a large deviation result for the pre-images of a point in the Julia set of a rational mapping of the Riemann sphere. As a corollary, we deduce a convergence result...
Poincaré series and zeta functions for surface group actions on R-trees (2007)
this paper could be adapted to provide a meromorphic extension in this more general setting
Error Terms for Closed Orbits of Hyperbolic Flows (2007)
this paper we shall consider error terms in estimates for the number of closed orbits for a large class of C flows # t : M M , restricted to a hyperbolic set #. Let #(T ) be the number of closed...
LINEAR ACTIONS OF FREE GROUPS Mark Pollicott and Richard Sharp (2007)
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...
Hausdorff Dimension And Asymptotic Cycles (2007)
We carry out a multifractal analysis for the asymptotic cycles for compact Riemann surfaces of genus g >= 2. This describes the set of unit tangent vectors for which the associated orbit has a...
Livsic Theorems, Maximizing Measures And The Stable Norm (2007)
In this article we consider two results motivated by Livsic's well known theorem that, for a hyperbolic system, a Holder continuous function is determined, up to a coboundary, by its values...
Growth Of Periodic Points And (2007)
Rotation Vectors On, Mark Pollicott, Richard Sharp
this paper will consider di#eomorphisms f : M M of a compact surface M , isotopic to the identity map, and study the growth of their periodic points. An important approach to studying such properties...
ASYMPTOTIC VERTEX GROWTH FOR GRAPHS Mark Pollicott (2007)
Introduction In this note, we want to describe a useful invariant for weighted graphs and characterize the minima of this quantity over all weightings which are suitably normalized. In the case of...
Topological dynamics of the Weil-Petersson geodesic flow (2007)
Pollicott, Mark, Weiss, Howard, Wolpert, Scott A.
We prove topological transitivity for the Weil Petersson geodesic flow for two-dimensional moduli spaces of hyperbolic structures. Our proof follows a new approach that exploits the density of...
Properties of measures supported on fat Sierpinski carpets (2006)
Jordan, Thomas, Pollicott, Mark
In this paper we study certain conformal iterated function schemes in two dimensions that are natural generalizations of the Sierpinski carpet construction. In particular, we consider scaling factors...
Positive-measure self-similar sets without interior (2006)
Csörnyei, M., Jordan, T., Pollicott, Mark, Preiss, David, Solomyak, B.
We recall the problem posed by Peres and Solomyak in Problems on self-similar and self-affine sets; an update. Progr. Prob. 46 (2000), 95–106: can one find examples of self-similar sets with...
Correlations for pairs of closed geodesics (2006)
Pollicott, Mark, Sharp, Richard
In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic estimates for pairs of closed geodesics, the differences of whose...
Countable state shifts and uniqueness of g-measures (2005)
Johansson, Anders, Öberg, Anders, Pollicott, Mark
In this paper we present a new approach to studying g-measures which is based upon local absolute continuity. We extend the result in [11] that square summability of variations of g-functions ensures...
Free Energy as a Geometric Invariant (2005)
The free energy plays a fundamental role in statistical and condensed matter physics. A related notion of free energy plays an important role in the study of hyperbolic dynamical systems. In this...
Livsic theorems, maximizing measures and the stable norm. (2004)
In this article we consider two results motivated by Livsic’s well known theorem that, for a hyperbolic system, a Hölder continuous function is determined, up to a coboundary, by its values around...
Abstract: Classical lattice spin systems provide an important and illuminating family of models in statistical physics. An interaction � on a lattice L ⊂ Zd determines a lattice spin system with...
Calculating Hausdorff dimension of Julia sets and Kleinian limit sets (2002)
Jenkinson, Oliver., Pollicott, Mark.
American Journal of Mathematics - Volume 124, Number 3, June 2002
Orthonormal Expansions of Invariant Densities for Expanding Maps (2002)
Oliver Jenkinson, Mark Pollicott
We give a novel way of constructing the density function for the absolutely continuous invariant measure of piecewise expanding C Markov maps. This is a classical problem, with one of the standard...
INVARIANCE PRINCIPLES FOR INTERVAL MAPS WITH AN INDIFFERENT FIXED POINT (2002)
In this note we establish an almost sure invariance principle for a large class of interval maps with indifferent fixed points, including the Manneville-Pomeau map. This implies a number of...
Livsic's Theorem for Semisimple Lie Groups (2001)
Nicol, Matthew, Pollicott, Mark
In this paper we show that strong generalizations of the measurable Livsic theorem for cocycles taking values in connected non-compact linear semisimple Lie groups, a canonical example being SL(2,R)...
Transitivity Of Euclidean Extensions Of Anosov Diffeomorphisms (2001)
We consider the class of extensions of Anosov di#eomorphisms on infranilmanifolds, and find necessary and su#cient conditions for topological transitivity. In particular, if the fiber is R, the...
In this paper we analyze a variant of the famous Schelling segregation model in economics as a dynamical system. This model exhibits, what appears to be, a new clustering mechanism. In particular, we...
Abstract: We extend some of the theory of multifractal analysis for conformal expanding systems to two new cases: The non-uniformly hyperbolic example of the Manneville– Pomeau equation and the...
Exponential error terms for growth functions on negatively curved surfaces (1998)
Sharp, Richard M., Pollicott, Mark.
American Journal of Mathematics - Volume 120, Number 5, October 1998
Asymptotic expansions for closed orbits in homology classes (1998)
Let V be a smooth compact manifold with rst Betti number b> 0 equipped with a Riemannian metric of (possibly variable) negative curvature. Such a manifold has a countable innity of closed...
Comparison theorems and orbit counting in hyperbolic geometry (1998)
Abstract. In this article we address an interesting problem in hyperbolic geometry. This is the problem of comparing different quantities associated to the fundamental group of a hyperbolic manifold...
Large deviations for maps with indifferent fixed points (1998)
Mark Pollicott, Richard Sharp, Michiko Yuri
We establish results on the distribution of pre-images with respect to the absolutely continuous invariant measure for certain systems with indifferent periodic points. This proves to be somewhat...
Comparison Theorems And Orbit Counting In Hyperbolic Geometry (1998)
In this article we address an interesting problem in hyperbolic geometry. This is the problem of comparing di#erent quantities associated to the fundamental group of a hyperbolic manifold (e.g. word...
Mark Pollicott, Richard Sharp, Michiko Yuri
We establish results on the distribution of pre-images with respect to the absolutely continuous invariant measure for certain systems with indi#erent periodic points. This proves to be somewhat more...
Exponential Error Terms For Growth Functions On Negatively Curved Surfaces (1998)
In this paper we consider two counting problems associated with compact negatively curved surfaces and improve classical asymptotic estimates due to Margulis. In the first, we show that the number of...
The circle problem on surfaces of variable negative curvature (1997)
Abstract. In this note we study the problem of orbit counting for certain groups of isometries of simply connected surfaces with possibly variable negative curvature. We show that if N(t) denotes the...
Periodic Orbits and Zeta Functions (1997)
Introduction 1 1. Twisted orbits and zeta functions 3 2. Axiom A dieomorphisms 4 3. Symbolic dynamics and rationality 5 4. Zeta functions and for interval maps 9 5. The Ruelle zeta function 14 6....
The Circle Problem on Surfaces of Variable Negative Curvature (1997)
In this note we study the problem of orbit counting for certain groups of isometries of simply connected surfaces with possibly variable negative curvature. We show that if N(t) denotes the orbit...
Poincaré series and comparison theorems for variable negative curvature (1994)
Poincar'e series have always played a central role in the theory of automorphic functions and harmonic analysis on manifolds of constant negative curvature. The trace formulae approach was...
Poincaré series and comparison theorems for variable negative curvature (1994)
Series And Comparison, Mark Pollicott, Richard Sharp
Introduction Poincare series have always played a central role in the theory of automorphic functions and harmonic analysis on manifolds of constant negative curvature. The trace formulae approach...
Lectures on ergodic theory and Pesin theory on compact manifols / Mark Pollicott (1993)
Incluye bibliografía e índice
Asymptotic Expansions For Closed Orbits In Homology Classes
this paper we concentrate on the distribution with respect to homology of V . A natural dynamical generalization of this problem is to study the distribution of closed orbits of Anosov flows, again...