Related papers: Categorical dynamical systems arising from sign-st…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
This paper examines and strengthens the Cuntz-Thomsen picture of equivariant Kasparov theory for arbitrary second-countable locally compact groups, in which elements are given by certain pairs of cocycle representations between C*-dynamical…
We establish a cluster theoretical interpretation of the isomorphisms of [F.-H.-O.-O., J. Reine Angew. Math., 2022] among quantum Grothendieck rings of representations of quantum loop algebras. Consequently, we obtain a quantization of the…
We continue the study of Rokhlin entropy, an isomorphism invariant for probability-measure-preserving actions of countable groups introduced in Part I. In this paper we prove a non-ergodic finite generator theorem and use it to establish…
Let $k$ be a field. We characterize the group schemes $G$ over $k$, not necessarily affine, such that $\mathsf{D}_{\mathrm{qc}}(B_kG)$ is compactly generated. We also describe the algebraic stacks that have finite cohomological dimension in…
Based on the convergence of their infinitesimal generators in the mixed topology, we provide a stability result for strongly continuous convex monotone semigroups on spaces of continuous functions. In contrast to previous results, we do not…
Lind and Schmidt have shown that the homoclinic group of a cyclic $\Z^k$ algebraic dynamical system is isomorphic to the dual of the phase group. We show that this duality result is part of an exact sequence if $k=1$. The exact sequence is…
Autonomous morphology, such as inflection class systems and paradigmatic distribution patterns, is widespread and diachronically resilient in natural language. Why this should be so has remained unclear given that autonomous morphology…
Given a categorical dynamical system, i.e. a triangulated category together with an endofunctor, one can try to understand the complexity of the system by computing the entropy of the endofunctor. Computing the entropy of the composition of…
We study a stochastic complex Ginzburg--Landau (CGL) equation driven by a smooth noise in space and we establish exponential convergence of the Markovian transition semi-group toward a unique invariant probability measure. Since Doob…
An estimation of the logarithmic timescale in quantum systems having an ergodic dynamics in the semiclassical limit of quasiclassical large parameters, is presented. The estimation is based on the existence of finite generators for ergodic…
We establish the equivalence between exponential decay of the relative entropy along a quantum Markov semigroup and the modified logarithmic Sobolev inequality for general von Neumann algebras. We also extend an intertwining criterion for…
In this expository paper we describe an unifying approach for many known entropies in Mathematics. First we recall the notion of semigroup entropy h_S in the category S of normed semigroups and contractive homomorphisms, recalling also its…
We consider the category of partially observable dynamical systems, to which the entropy theory of dynamical systems extends functorially. This leads us to introduce quotient-topological entropy. We discuss the structure that emerges. We…
Discrete stationary classical processes as well as quantum lattice states are asymptotically confined to their respective typical support, the exponential growth rate of which is given by the (maximal ergodic) entropy. In the iid case the…
We propose the entropy estimator $H_Z$, calculated from global dynamical parameters, in an attempt to capture the degree of evolution of galaxy systems. We assume that the observed (spatial and velocity) distributions of member galaxies in…
We present a construction of stable diagonal factorizations, used to define categorical models of type theory with identity types, from a family of algebraic weak factorization systems on the slices of a category. Inspired by a…
We classify self-injective radical cube zero algebras with respect to whether they satisfy certain finite generation conditions sufficient to have a fruitful theory of support varieties defined via Hochschild cohomology in the vein of…
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…
We introduce and study a class of discrete particle ensembles that naturally arise in connection with classical random matrix ensembles, log-gases and Jack polynomials. Under technical assumptions on a general analytic potential we prove…