Related papers: Real entropy rigidity under quasi-conformal deform…

Let $R$ be a ring, let $G$ be an amenable group and let $R\ast G$ be a crossed product. The goal of this paper is to construct, starting with a suitable additive function $L$ on the category of left modules over $R$, an additive function on…

Let $G$ and $\tilde G$ be Kleinian groups whose limit sets $S$ and $\tilde S$, respectively, are homeomorphic to the standard Sierpi\'nski carpet, and such that every complementary component of each of $S$ and $\tilde S$ is a round disc. We…

We derive an upper bound on the maximum balanced bipartite entanglement entropy of ground states of many-body Hamiltonians defined on a graph, agnostic to any particular model, that possesses a nontrivial automorphism group. We show that…

We obtain sharp rotation bounds for the subclass of homeomorphisms $f:\mathbb{C}\to\mathbb{C}$ of finite distortion which have distortion function in $L^p_{loc}$, $p>1$, and for which a H\"older continuous inverse is available. The interest…

In this paper, we determine the topological entropy $h(\phi)$ of a continuous endomorphism $\phi$ of a Lie group $G$. This computation is a classical topic in ergodic theory which seemed to have long been solved. But, when $G$ is…

We establish orbit equivalence rigidity for any ergodic, essentially free and measure-preserving action on a standard Borel space with a finite positive measure of the mapping class group for a compact orientable surface with higher…

We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at infinity on any of these latter examples,…

In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…

The first aims of this work are to endorse the advent of finitely additive set functions as equilibrium states and the possibility to replace the metric entropy by an upper semi-continuous map associated to a general variational principle.…

We establish the following Hadamard--Stoker type theorem: Let $f:M^n\rightarrow\mathscr{H}^n\times\mathbb R$ be a complete connected hypersurface with positive definite second fundamental form, where $\mathscr H^n$ is a Hadamard manifold.…

For a fixed topological Markov shift, we consider measure-preserving dynamical systems of Gibbs measures for 2-locally constant functions on the shift. We also consider isomorphisms between two such systems. We study the set of all…

Let $M$ be a compact, connected manifold of positive dimension and let $\mathcal G\leq\textrm{Homeo}(M)$ be \emph{locally approximating} in the sense that for all open $U\subseteq M$ compactly contained in a single Euclidean chart of $M$,…

In this paper we obtain exact normal forms with functional invariants for local diffeomorphisms, under the action of the symplectomorphism group in the source space. Using these normal forms we obtain exact classification results for the…

We show that given a quasi-circle $C$ in $\partial_{\infty}\mathbb{H}^3$ (respectively in $\partial_{\infty} \mathbb{ADS}^3$) and a complete conformal metric $h$ on $\mathbb{D}$ whose curvature $K_h$ takes values in a compact subset of…

For a class of $\zz^2$ Markov Random Fields (MRFs) $\mu$, we show that the sequence of successive differences of entropies of induced MRFs on strips of height $n$ converges exponentially fast (in $n$) to the entropy of $\mu$. These strip…

The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…

Consider a statistical physical model on the $d$-regular infinite tree $T_{d}$ described by a set of interactions $\Phi$. Let $\{G_{n}\}$ be a sequence of finite graphs with vertex sets $V_n$ that locally converge to $T_{d}$. From $\Phi$…

We show some preservation results of amenably extending strongly Ulam stable groups under mild decay assumptions, including quantitative preservation of asymptotic bounds under the assumption that the modulus of stability is H\"older…

In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…

We present an accurate and efficient framework for real-space Hubbard-corrected density functional theory. In particular, we obtain expressions for the energy, atomic forces, and stress tensor suitable for real-space finite-difference…