Related papers: A note on arithmetic topology and dynamical system…
We introduce and study a notion of algebraic entropy for self-maps of finite length of Noetherian local rings, and develop its properties. We show that it shares the standard properties of topological entropy. For finite self-maps we…
A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be…
We afford the problem of counting the blocks of a given length made with symbols drawn from an alphabet and relate this number to Fibonacci-like recurrent relations. The recurrence polynomia allows to calculate the limit ratio of two…
We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…
In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable…
In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as…
The collection of all topologies on the set of three points is studied treating the topology as quantum-like observable. It turns out to be possible under the assumption of the asymmetry between the spaces of bra- and ket-vectors. The…
In this note we give a re-interpretation of the algebraic fundamental group for proper schemes that is rather close to the original definition of the fundamental group for topological spaces. The idea is to replace the standard interval…
Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a…
Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have…
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I…
We show that there is a stable homotopy theory of profinite spaces and use it for two main applications. On the one hand we construct an \'etale topological realization of the stable motivic homotopy theory of smooth schemes over a base…
A consistent set of six integrable discrete and continuous dynamical systems are suggested corresponding to arbitrary affine Lie algebra. The set contains a system of partial differential equations which can be treated as a version of…
In this paper we study topological entropy and recurrence properties of non-autonomous dynamical system generated by a family of continuous self maps on a compact space X. Specially, we introduce the pseudo-entropy and…
Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…
In this note we relate three topics for arithmetic schemes: a general duality for \'etale constructible torsion sheaves, an \'etale homology theory, and a Gersten-Bloch-Ogus-Kato complex. The results in this paper have been used in other…
The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system…
To each dynamic equivalence of two control systems is associated an infinite permutation matrix. We investigate how such matrices are related to the existence of dynamic equivalences.
Alternative set theory (AST) may be suitable for the ones who try to capture objects or phenomenons with some kind of indefiniteness of a border. While AST provides various notions for advanced mathematical studies, correspondence of them…