Related papers: Primes, knots and periodic orbits
A dynamic sieve method is designed according to the basic sieve method. It mainly refers to the symbolic dynamics theory. By this method, we could connect the prime system with familiar 'Logistic Mapping'. An interesting discovery is that…
In this paper, the study of the global orbit pattern (gop) formed by all the periodic orbits of discrete dynamical systems on a finite set $X$ allows us to describe precisely the behaviour of such systems. We can predict by means of closed…
The most tight conformations of prime knots are found with the use of the SONO algorithm. Their curvature and torsion profiles are calculated. Symmetry of the knots is analysed. Connections with the physics of polymers are discussed.
We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. The dynamics for arities of…
This paper employs various computational techniques to determine the bridge numbers of both classical and virtual knots. For classical knots, there is no ambiguity of what the bridge number means. For virtual knots, there are multiple…
The phase diagram of a simple area-preserving map, which was motivated by the quantum dynamics of cold atoms, is explored analytically and numerically. Periodic orbits of a given winding ratio are found to exist within wedge-shaped regions…
We study algebraic tangles as fundamental components in knot theory, developing a systematic approach to classify and tabulate prime tangles using a novel canonical representation. The canonical representation enables us to distinguish…
We describe an algebra for composing automata which includes both classical and quantum entities and their communications. We illustrate by describing in detail a quantum protocol.
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory.
We study the algebraic dynamical systems generated by triangular systems of rational functions and estimate the height growth of iterations generated by such systems. Further, using a result on the reduction modulo primes of systems of…
We discuss analogies between number theory and the theory of dynamical systems on spaces with a one-codimensional foliation. The emphasis is on comparing the "explicit formulas" of analytic number theory with certain dynamical Lefschetz…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
This note aims to offer a non-technical and self-contained introduction to gravitational algebras and their applications in the nonequilibrium physics of gravitational systems. We begin by presenting foundational concepts from operator…
This paper is devoted to prove the existence of $q$-periodic alternating projections of prime alternating $q$-periodic knots. The main tool is the Menasco-Thistlethwaite's Flyping theorem. Let $K$ be an oriented prime alternating knot that…
The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
Quantum algorithms are built enabling to find Poincar\'e recurrence times and periodic orbits of classical dynamical systems. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of…
We introduce a new numerical invariant of knots and links from the descending diagrams. It is considered to live between the unknotting number and the bridge number.
In this paper, we obtained a class of oscillatory, cyclic and knot type solutions from the non-linear Friedmann equations. This is performed by choosing specific forms of energy density and pressure of matter. All the expressions written…
There are many analogies between codes, lattices, and vertex operator algebras. For example, extremal objects are good examples of combinatorial, spherical, and conformal designs. In this study, we investigated these objects from the aspect…