Related papers: Exploring the Dynamics of the Circumcenter Map
We study the dynamics of the attractor of the doubling map with an asymmetrical hole by associating to each hole an element of the lexicographic world. A description of the topological entropy function is given. We show that the set of…
Motivated by the centering of biological objects in large cells, we study the generic properties of centering forces inside a ball (or a volume of spherical topology) in $n$ dimensions. We consider two scenarios : autonomous centering (in…
Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide…
This paper points out the usefulness of the concept of derivation along a map in many problems in Geometry and Physics. In particular it will be shown that this approach allows us to translate the usual concepts arising in Geometrical…
Inspired by a twist maps theorem of Mather we study recurrent invariant sets that are ordered like rigid rotation under the action of the lift of a bimodal circle map $g$ to the $k$-fold cover. For each irrational in the interior of the…
Symplectic maps are routinely used to describe single-particle dynamics in circular accelerators. In the case of a linear accelerator map, the rotation number (the betatron frequency) can be easily calculated from the map itself. In the…
This paper presents a survey of recent and not so recent results concerning the study of smooth homeomorphisms of the circle with a finite number of non-flat critical points, an important topic in the area of One-dimensional Dynamics. We…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichm\"uller space…
We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic…
Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…
The internal motions of biomatter immersed in biofluid are investigated. The interactions between the fragments of biomatter and its surrounding biofluid are modeled using field theory. In the model, the biomatter is coupled to the gauge…
In this paper, several fundamental facts, especially the existence and uniqueness of an absolutely continuous ergodic measure with an exponential mixing rate, are derived for smooth expanding circle maps. Although the results are classical,…
Representing a scanned map of the real environment as a topological structure is an important research topic in robotics. Since topological representations of maps save a huge amount of map storage space and online computing time, they are…
This paper introduces the \textit{truncator} map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify…
This paper studies the properties of convergence of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semi-cyclic impulsive self-mappings on the union of a number of nonempty…
Vertically stacked exchange coupled magnetic heterostructures of cylindrical geometry can host complex noncolinear magnetization patterns. By tuning the interlayer exchange coupling between a layer accommodating magnetic vortex state and an…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
We examine the onset of classical topological order in a nearest-neighbor kagome ice model. Using Monte Carlo simulations, we characterize the topological sectors of the groundstate using a non-local cut measure which circumscribes the…