Related papers: Algebraic entropy of sign-stable mutation loops
We establish basic properties of cluster algebras associated with oriented bordered surfaces with marked points. In particular, we show that the underlying cluster complex of such a cluster algebra does not depend on the choice of…
We construct a natural invariant measure concentrated on the set of square-free numbers, and invariant under the shift. We prove that the corresponding dynamical system is isomorphic to a translation on a compact, Abelian group. This…
We consider two kinds of periodicities of mutations in cluster algebras. For any sequence of mutations under which exchange matrices are periodic, we define the associated T- and Y-systems. When the sequence is `regular', they are…
Richard Eager and Sebastian Franco introduced a change of basis transformation on the F-polynomials of Fomin and Zelevinsky, corresponding to rewriting them in the basis given by fractional brane charges rather than quiver gauge groups.…
Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of…
Since the discovery of molecular resonances in $^{12}$C+$^{12}$C in the early sixties a great deal of research work has been undertaken to study alpha-clustering. Our knowledge on physics of nuclear molecules has increased considerably and…
Let $G$ be the group $\mathbb{Z}^d$ or the monoid $\mathbb{N}^d$ where $d$ is a positive integer. Let $X$ be a subshift over $G$, i.e., a closed and shift-invariant subset of $A^G$ where $A$ is a finite alphabet. We prove that the…
The Shannon entropy of a random variable has much behaviour analogous to a signed measure. Previous work has explored this connection by defining a signed measure on abstract sets, which are taken to represent the information that different…
This if the final paper in the seriesContinuous Quivers of Type $A$. In this part, we generalize existing geometric models of type $A$ cluster structures to the new $\mathbf E$-clusters introduced in part (III). We also introduce an…
For any discrete time dynamical system with a rational evolution, we define an entropy, which is a global index of complexity for the evolution map. We analyze its basic properties and its relations to the singularities and the…
We study the connection between the appearance of a `metastable' behavior of weakly chaotic orbits, characterized by a constant rate of increase of the Tsallis q-entropy (Tsallis 1988), and the solutions of the variational equations of…
A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit…
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…
Assume that a sequence $x=x_0x_1\ldots$ is frequency-typical for a finite-valued stationary stochastic process $\textbf X$. We prove that the function associating to $x$ the entropy-rate $\bar H(\textbf X)$ of $\textbf X$ is uniformly…
The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, such constant was proven to exist, under the assumption of a…
Given ergodic p-invariant measures {\mu_i} on the 1-torus T=R/Z, we give a sharp condition on their entropies, guaranteeing that the entropy of the convolution \muon converges to \log p. We also prove a variant of this result for joinings…
We prove a multiplication formula for cluster characters induced by generating extensions in a gentle algebra A, generalizing a result of Cerulli Irelli, Esposito, Franzen, Reineke. In the case where A is the gentle algebra of a…
One of the remarkable properties of cluster algebras is that any cluster, obtained from a sequence of mutations from an initial cluster, can be written as a Laurent polynomial in the initial cluster (known as the "Laurent phenomenon").…
Recently, clustering of inertial particles in turbulence has been thoroughly analyzed for statistically homogeneous isotropic flows. Phenomenologically, spatial homogeneity of particles configurations is broken by the advection of a range…
We consider quivers/skew-symmetric matrices under the action of mutation (in the cluster algebra sense). We classify those which are isomorphic to their own mutation via a cycle permuting all the vertices, and give families of quivers which…