Related papers: Dynamics on fences

This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…

Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the category of smooth manifolds. They provide an abstract…

Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…

This article consists in applications of [arXiv:2511.14232] in the case of homemomorphisms of higher genus surfaces whose homological rotation set is big enough -- a class of dynamics that is open. We first prove a structure theorem for the…

This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…

We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…

In this work we develop a new criterion for the existence of topological horseshoes for surface homeomorphisms in the isotopy class of the identity. Based on our previous work on forcing theory, this new criterion is purely topological and…

The discovery of topological matter has revolutionized the field of condensed matter physics giving rise to many interesting phenomena, and fostering the development of new quantum technologies. In this thesis we study the quantum dynamics…

We describe a self-homeomorphism $R$ of the Cantor set $X$ and then show that its conjugacy class in the Polish group $H(X)$ of all homeomorphisms of $X$ forms a dense $G_\delta$ subset of $H(X)$. We also provide an example of a locally…

Let f be a hyperbolic transcendental entire function of finite order in the Eremenko-Lyubich class (or a finite composition of such maps), and suppose that f has a unique Fatou component. We show that the Julia set of $f$ is a Cantor…

We describe the approximation of a continuous dynamical system on a p. l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background…

Knots naturally appear in continuous dynamical systems as flow periodic trajectories. However, discrete dynamical systems are also closely connected with the theory of knots and links. For example, for Pixton diffeomorphisms, the…

We consider heavy-tailed observables maximised on a dynamically defined Cantor set and prove convergence of the associated point processes as well as functional limit theorems. The Cantor structure, and its connection to the dynamics,…

Topological theories have established a new set of rules that govern the transport properties in a wide variety of wave-mechanical settings. In a marked departure from the established approaches that induce Floquet topological phases by…

This paper concerns the link between the dynamical behaviour of a dynamical system and the dynamical behaviour of its numerical simulations. Here, we model numerical truncation as a spatial discretization of the system. Some previous works…

We introduce a class of diffeological spaces, called elastic, on which the left Kan extension of the tangent functor of smooth manifolds defines an abstract tangent functor in the sense of Rosicky. On elastic spaces there is a natural…

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $ N $ variables, as binary neural networks and cellular automata. The main difficulty is the…

We continue to study topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology tau, which was started in the paper (S. Bezuglyi, A.H. Dooley, and J. Kwiatkowski, Topologies on…

We derive a necessary and sufficient condition for a homeomorphism with the shadowing property to be topologically transitive: to have an invariant subset $A$, dense in the non-wandering set, where the barycenter property holds. To…

For many transcendental entire functions, the escaping set has the structure of a Cantor bouquet, consisting of uncountably many disjoint curves. Rippon and Stallard showed that there are many functions for which the escaping set has a new…