Related papers: Sharkovsky's Ordering in the Mandelbrot Set
Periodic orbit action correlations are studied for the piecewise linear, area-preserving Baker map. Semiclassical periodic orbit formulae together with universal spectral statistics in the corresponding quantum Baker map suggest the…
The scope of this paper is two-fold. First, to present to the researchers in combinatorics an interesting implementation of permutations avoiding generalized patterns in the framework of discrete-time dynamical systems. Indeed, the orbits…
We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…
An algebraic tree T is one determined by a finite system of fixed point equations. The frontier \Fr(T) of an algebraic tree t is linearly ordered by the lexicographic order \lex. When (\Fr(T),\lex) is well-ordered, its order type is an…
We attribute the structural phase transition (SPT) in the parent compounds of the iron pnictides to orbital ordering. Due to the anisotropy of the $d_{xz}$ and $d_{yz}$ orbitals in the $xy$ plane, a ferro-orbital ordering makes the…
In this paper we will refine Sacksteder's theorem for groups of orientation-preserving homeomorphisms of the circle in the case that there exists a finite orbit set. We will give a categorization of the topological possibilities for the…
Li-York theorem tells us that a period 3 orbit for a continuous map of the interval into itself implies the existence of a periodic orbit of every period. This paper concerns an analogue of the theorem for homeomorphisms of the…
An extension of order theory is presented that serves as a formalism for the study of dendroidal sets analogously to way the formalism of order theory is used in the study of simplicial sets.
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
Direct look at the celebrated "chaotic" Mandelbrot Set in Fig..\ref{Mand2} immediately reveals that it is a collection of almost ideal circles and cardioids, unified in a specific {\it forest} structure. In /hep-th/9501235 a systematic…
An algebraic linear ordering is a component of the initial solution of a first-order recursion scheme over the continuous categorical algebra of countable linear orderings equipped with the sum operation and the constant 1. Due to a general…
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…
These notes were written during the 9th and 10th sessions of the subject Dynamical Systems II coursed at DTU (Denmark) during the Winter Semester 2015-2016, and later extended in February 2017. They aim to provide students with a…
As shown by A. Melnikov, the orbits of a Borel subgroup acting by conjugation on upper-triangular matrices with square zero are indexed by involutions in the symmetric group. The inclusion relation among the orbit closures defines a partial…
We introduce a new tool, called the orbit automaton, that describes the action of an automaton group $G$ on the subtrees corresponding to the orbits of $G$ on levels of the tree. The connection between $G$ and the groups generated by the…
Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In…
We study a circular order on labelled, m-edge-coloured trees with k vertices, and show that the set of such trees with a fixed circular order is in bijection with the set of RNA m-diagrams of degree k, combinatorial objects which can be…
We give an alternate proof of the left-orderability of the mapping class group of a connected oriented infinite-type surface with a non-empty boundary. Our main strategy involves the inductive construction of a countable stable Alexander…
We arrange the orders in an algebraic number field in a tree. This tree can be used to enumerate all orders of bounded index in the maximal order as well as the orders over some given order.
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…