Related papers: On Relative Category and Morse Decompositions for …
We construct dendrites with endpoint sets isometric to any totally disconnected compact metric space. This allows us to embed zero-dimensional dynamical systems into dendrites and solve a problem regarding Li-Yorke and distributional chaos.
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…
Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain…
We extend the Watanabe--Sagawa--Ueda (WSU) uncertainty relations for measurement errors to infinite-dimensional systems. The original WSU formulation provided a definition of measurement errors with a clear physical interpretation based on…
The (e,n)-complexity functions describe total instability of trajectories in dynamical systems. They reflect an ability of trajectories going through a Borel set to diverge on the distance $\epsilon$ during the time interval n. Behavior of…
In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described…
Structure and properties of families of critical points for classes of functions $W(z,\bar{z})$ obeying the elliptic Euler-Poisson-Darboux equation $E(1/2,1/2)$ are studied. General variational and differential equations governing the…
In this article, we introduce a notion of relative mean metric dimension with potential for a factor map $\pi: (X,d, T)\to (Y, S)$ between two topological dynamical systems. To link it with ergodic theory, we establish four variational…
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to…
Motivated by work of Kucharczyk and Scholze, we use sheafified rational Witt vectors to attach a new ringed space $W_{\mathrm{rat}} (X)$ to every scheme $X$. We also define $R$-valued points $W_{\mathrm{rat}} (X) (R)$ of $W_{\mathrm{rat}}…
We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…
We investigate the entanglement between two separated segments in the vacuum state of a free 1D Klein-Gordon field, where explicit computations are performed in the continuum limit of the linear harmonic chain. We show that the…
We construct invariants of relative K-theory classes of multiparameter dependent pseudodifferential operators, which recover and generalize Melrose's divisor flow and its higher odd-dimensional versions of Lesch and Pflaum. These higher…
In various situations in Floer theory, one extracts homological invariants from "Morse-Bott" data in which the "critical set" is a union of manifolds, and the moduli spaces of "flow lines" have evaluation maps taking values in the critical…
We study dissipative dynamics constructed by means of non-commutative Dirichlet forms for various lattice systems with multiparticle interactions associated to CCR algebras. We give a number of explicit examples of such models. Using an…
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…
We classify C$^*$ near-group categories by using Vaughan Jones theory of subfactors and the Cuntz algebra endomorphisms. Our results show that there is a sharp contrast between two essentially different cases, integral and irrational cases.…
For an $(\infty,n)$-category $\mathscr E$ we define an $(\infty,1)$ category $\mathrm{TwAr}(\mathscr E)$ and provide an isomorphism between the stabilization of the overcategory of $\mathscr E$ in $\mathrm{Cat}_{(\infty,n)}$ and the…
The paper deals with convergence of solutions of a class of stochastic differential equations driven by infinite-dimensional semimartingales. The infinite-dimensional semimartingales considered in the paper are Hilbert-space valued. The…