Related papers: The bifurcation measure is exponentially mixing

We show that the measure of maximal entropy of every complex H\'enon map is exponentially mixing of all orders for H\''older observables. As a consequence, the Central Limit Theorem holds for all H\''older observables.

Given a pseudo-Riemannian metric of regularity $C^{1,1}$ on a smooth manifold, we prove that the corresponding exponential map is a bi-Lipschitz homeomorphism locally around any point. We also establish the existence of totally normal…

We construct extremal metrics on the total space of certain destabilising test configurations for strictly semistable K\"ahler manifolds. This produces infinitely many new examples of manifolds admitting extremal K\"ahler metrics. It also…

We prove that given any $\theta_1,\ldots,\theta_{2d-2}\in \R\setminus\Z$, the support of the bifurcation measure of the moduli space of degree $d$ rational maps coincides with the closure of classes of maps having $2d-2$ neutral cycles of…

We investigate the geometry of the maximal a posteriori (MAP) partition in the Bayesian Mixture Model where the component and the base distributions are chosen from conjugate exponential families. We prove that in this case the clusters are…

We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…

We study critical orbits and bifurcations within the moduli space of quadratic rational maps on $\mathbb{P}^1$. We focus on the family of curves, $Per_1(\lambda)$ for $\lambda$ in $\mathbb{C}$, defined by the condition that each $f\in…

We develop the study of some spaces of currents of bidegree (p,p). As an application we construct the equilibrium measure for a large class of birational maps of P^k as intersection of Green currents. We show that these currents are…

We prove that every locally pluripolar set on a compact complex manifold is pluripolar. This extends similar results in K\"ahler case.

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…

We show that any dominant meromorphic self-map f of a compact Kaehler manifold X is an Artin-Mazur map. More precisely, if P_n(f) is the number of its isolated periodic points of period n (counted with multiplicity), then P_n(f) grows at…

We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…

We study the dynamics of the Teichmuller flow in the moduli space of Abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant…

For mappings in metric spaces satisfying one inequality with respect to modulus of families of curves, there is proved a lightness of the uniform limit of these mappings. It is proved that, the uniform limit of these mappings is light…

As a generalization of Hausdorff's extension theorem of metrics, we prove an interpolation theorem of a family of metrics defined on closed subsets of metrizable spaces. As an application, we investigate typicality of subsets of moduli…

Let S be a non-exceptional oriented surface of finite type. We give a new proof based on symbolic coding of the following result of Avila and Gouezel. The Teichmueller flow is exponentially mixing with respect to any ergodic…

We study extensions of the measure of maximal entropy to suitable compactifications of the parameter space and the moduli space of rational maps acting on the Riemann sphere. For parameter space, we consider a space which resolves the…

We consider skew extensions of expanding maps by compact Lie groups. For a class of natural invariant measures, we prove an explicit lower bound on the rate of (exponential) mixing involving topological pressure. Proof uses representation…

In this paper, several fundamental facts, especially the existence and uniqueness of an absolutely continuous ergodic measure with an exponential mixing rate, are derived for smooth expanding circle maps. Although the results are classical,…

We show that measures of irrationality on very general codimension two complete intersections and very general complete intersection surfaces are multiplicative in the degrees of the defining equations. This confirms some cases of a…