Related papers: Universal functions for the Sharkovsky classes of …
This paper discusses a more general contractive condition for a class of extended cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same…
We extend Sharkovskii's theorem to the cases of $N$-dimensional maps which are close to 1D maps, with an attracting $n$-periodic orbit. We prove that, with relatively weak topological assumptions, there exist also $m$-periodic orbits for…
In the author's PhD thesis (2019) universal envelopes were introduced as a tool for studying the continuously obtainable information on discontinuous functions. To any function $f \colon X \to Y$ between $\operatorname{qcb}_0$-spaces one…
We consider dynamical systems given by interval maps with a finite number of turning points (including critical points, discontinuities) possibly of different critical orders from two sides. If such a map $f$ is continuous and piecewise…
We find universal spaces for Alexandroff and finite spaces and explore some of its topological properties as well as their description as inverse limits of finite spaces and Alexandroff extensions. They can be used as a natural environment…
We study the asymptotical behaviour of iterates of piecewise contractive maps of the interval. It is known that Poincar\'e first return maps induced by some Cherry flows on transverse intervals are, up to topological conjugacy, piecewise…
We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the system is close to a one-dimensional map in a certain sense.…
In this present article, we get sufficient conditions for the existence and uniqueness of fixed points and common fixed points for single and double mapping satisfying various contractive conditions within the partially ordered…
A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and…
We consider some smooth maps on a bouquet of circles. For these maps we can compute the number of fixed points, the existence of periodic points and an exact formula for topological entropy. We use Lefschetz fixed point theory and actions…
We prove that for continuous maps on the interval, the existence of an n-cycle, implies the existence of n-1 points which interwind the original ones and are permuted by the map. We then use this combinatorial result to show that piecewise…
We show that the class of trapezoid orders in which no trapezoid strictly contains any other trapezoid strictly contains the class of trapezoid orders in which every trapezoid can be drawn with unit area. This is different from the case of…
A global vector field $v$ on a "spacetime" differentiable manifold $\mathrm{V}$, of dimension $N+1$, defines a congruence of world lines: the maximal integral curves of $v$, or orbits. The associated global space $\mathrm{N}\_v$ is the set…
In this paper, we establish some common fixed point results for a new class of pair of contractions mappings having functions as contractive parameters, and satisfying certain commutative properties.
In this article, we study the behaviour of discrete one-dimensional dynamical systems associated to functions on finite sets. We formalise the global orbit pattern formed by all the periodic orbits (gop) as the ordered set of periods when…
This article first answers to questions about connectedness of a new family of graphs on unicellular maps. Answering these questions goes through a description of the mapping class group as surgeries on unicellular maps. We also show how…
We prove that for every $d\geq 3$ the homomorphism order of the class of line graphs of finite graphs with maximal degree $d$ is universal. This means that every finite or countably infinite partially ordered set may be represented by line…
Both the Wavefunction of the Universe and the Schwinger-Keldysh in-in formalism are central tools for analyzing primordial cosmological observables, such as equal-time correlation functions. While their conceptual equivalence is well…
In this paper we are going to prove a very general fixed point theorem for mappings acting in partial metric spaces. In that theorem we impose some conditions on behavior of considered mappings on orbits and a condition relating orbits of…
In this paper, we study the existence of fixed points for mappings defined on complete metric space (X, d) satisfying a general contractive inequality of integral type depended on another function. This conditions is analogous of Banach…