44 research outputs found
Non trivial limit distributions for transient renewal chains
In this work we study the asymptotic of renewal sequences associated with
certain transient renewal Markov chains and enquire about the existence of
limit laws in this set up
Local limit theorems for suspended semiflows
We prove local limit theorems for a cocycle over a semiflow by establishing
topological, mixing properties of the associated skew product semiflow. We also
establish conditional rational weak mixing of certain skew product semiflows
and various mixing properties including order 2 rational weak mixing of
hyperbolic geodesic flows of cyclic covers.Comment: Various corrections & dedication added. 45 page
Upper and lower bounds for the correlation function via inducing with general return times
For non-uniformly expanding maps inducing with a general return time to Gibbs
Markov maps, we provide sufficient conditions for obtaining higher order
asymptotics for the correlation function in the infinite measure setting. Along
the way, we show that these conditions are sufficient to recover previous
results on sharp mixing rates in the finite measure setting for non-Markov
maps, but for a larger class of observables. The results are illustrated by
(finite and infinite measure preserving) non-Markov intervals maps with an
indifferent fixed point
Operator renewal theory for continuous time dynamical systems with finite and infinite measure
We develop operator renewal theory for flows and apply this to obtain results
on mixing and rates of mixing for a large class of finite and infinite measure
semiflows. Examples of systems covered by our results include suspensions over
parabolic rational maps of the complex plane, and nonuniformly expanding
semiflows with indifferent periodic orbits. In the finite measure case, the
emphasis is on obtaining sharp rates of decorrelations, extending results of
Gou\"ezel and Sarig from the discrete time setting to continuous time. In the
infinite measure case, the primary question is to prove results on mixing
itself, extending our results in the discrete time setting. In some cases, we
obtain also higher order asymptotics and rates of mixing.Comment: Final version, to appear in Monatsh. Mat
Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure
We prove results on mixing and mixing rates for toral extensions of
nonuniformly expanding maps with subexponential decay of correlations. Both the
finite and infinite measure settings are considered. Under a Dolgopyat-type
condition on nonexistence of approximate eigenfunctions, we prove that existing
results for (possibly nonMarkovian) nonuniformly expanding maps hold also for
their toral extensions.Comment: Final version, published in J. Mod. Dy
Decay of correlations for nonuniformly expanding systems with general return times
We give a unified treatment of decay of correlations for nonuniformly
expanding systems with a good inducing scheme. In addition to being more
elementary than previous treatments, our results hold for general integrable
return time functions under fairly mild conditions on the inducing scheme