Related papers: Lipschitz regularity of the invariant measure of r…
In this paper it is shown that if $\mu$ is an n-dimensional Ahlfors-David regular measure in $R^d$ which satisfies the so-called weak constant density condition, then $\mu$ is uniformly rectifiable. This had already been proved by David and…
In this work we study certain invariant measures that can be associated to the time averaged observation of a broad class of dissipative semigroups via the notion of a generalized Banach limit. Consider an arbitrary complete separable…
We show how the small perturbations of a linear cocycle have a relative rotation number associated with an invariant measure of the base dynamics an with a $2$-dimensional bundle of the finest dominated splitting (provided that some…
We study the behavior of a three-dimensional dynamical system with respect to some set $S$ given in 3-dimensional euclidian space. Geometrically such a system arises from the normalized Ricci flow on some class of generalized Wallach spaces…
Robustness measures are increasingly prominent resource quantifiers that have been introduced for quantum resource theories such as entanglement and coherence. Despite the generality of these measures, their usefulness is hindered by the…
We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in \cite{bacry} . If M is a non degenerate multifractal measure with associated metric $\rho(x,y)=M([x,y])$ and structure function…
A large class of hyperbolic and parabolic partial differential equation (PDE) systems, such as reaction-diffusion processes, when expressed in the infinite-dimensional (Inf-D) framework can be represented as Riesz spectral (RS) systems.…
We consider a class of piecewise hyperbolic maps from the unit square to itself preserving a contracting foliation and inducing a piecewise expanding quotient map, with infinite derivative (like the first return maps of Lorenz like flows).…
In traditional work on numerical schemes for solving stochastic differential equations (SDEs), it is usually assumed that the coefficients are globally Lipschitz. This assumption has been used to establish a powerful analysis of the…
We shall study in this paper the Lipschitz type stabilities and convergence rates of Tikhonov regularization for the recovery of the radiativities in elliptic and parabolic systems with Dirichlet boundary conditions. The Lipschitz type…
In [Gwiazda, Jamr\'oz, Marciniak-Czochra 2012] a framework for studying cell differentiation processes based on measure-valued solutions of transport equations was introduced. Under application of the so-called measure-transmission…
In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, $T$, in a product space whose alphabet is a perfect and separable metric space (thus,…
In skew-product systems with contractive factors, all orbits asymptotically approach the graph of the so-called sync function; hence, the corresponding regularity properties primarily matter. In the literature, sync function Lipschitz…
By using a classical truncated argument and introducing the local Wasserstein distance, the global existence and uniqueness are proved for the distribution dependent SDEs with local Lipschitz coefficients. Due to the measure dependence, the…
Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to…
We study invariant measures for random countable (finite or infinite) conformal iterated function systems (IFS) with arbitrary overlaps. We do not assume any type of separation condition. We prove, under a mild assumption of finite entropy,…
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
Pesin's formula relates the entropy of a dynamical system with its positive Lyapunov exponents. It is well known, that this formula holds true for random dynamical systems on a compact Riemannian manifold with invariant probability measure…
Using the coupling method introduced in \cite{Geiss:Ylinen:21}, we investigate regularity properties of stochastic differential equations, where we consider the Lipschitz case in $\R^d$ and allow for H\"older continuity of the diffusion…
We prove a local Lipschitz stability estimate for Gel'fand-Calder\'on's inverse problem for the Schr\"odinger equation. The main novelty is that only a finite number of boundary input data is available, and those are independent of the…