Related papers: Constant Slope Maps on the Extended Real Line

We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when it is not true.

This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…

In this paper, we introduce a generalized piecewise translation map on the Euclidean space. We provide a special case when this map is always of finite type. For a finite type map in this case, we form conjectures on the semi-continuity of…

An argument is given to associate integrable nonintegrable transition of discrete maps with the transition of Lawvere's fixed point theorem to its own contrapositive. We show that the classical description of nonlinear maps is neither…

Some fixed point results are given for a class of Meir-Keeler contractive maps acting on metric spaces endowed with locally transitive relations. Technical connections with the related statements due to Berzig et al [Abstr. Appl. Anal.,…

Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When…

A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…

We study periodic, piecewise linear maps on the plane starting with the Mort Brown's map. We show that if the number of pieces is two, there is only a short list of possible periods (this fact can be seen as the crystallographic restriction…

We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation…

A consistent path system in a graph $G$ is an collection of paths, with exactly one path between any two vertices in $G$. A path system is said to be consistent if it is intersection-closed. We say that $G$ is strictly metrizable if every…

We study the dependence of the topological entropy of piecewise monotonic maps with holes under perturbations, for example sliding a hole of fixed size at uniform speed or expanding a hole with uniform expansion. We show that under suitable…

We determine the probability thresholds for the existence of monotone paths, of finite and infinite length, in random oriented graphs with vertex set $\mathbb N^{[k]}$, the set of all increasing $k$-tuples in $\mathbb N$. These graphs…

This is an outline of work in progress. We study the conjecture that the topological entropy of a real cubic map depends ``monotonely'' on its parameters, in the sense that each locus of constant entropy in parameter space is a connected…

We show by example that there is a Cayley graph, having two invariant random subgraphs X and Y, such that there exists a monotone coupling between them in the sense that $X\subset Y$, although no such coupling can be invariant. Here,…

A conjugate skew gain graph is a skew gain graph with the labels (also called, the conjugate skew gains) from the field of complex numbes on the oriented edges such that they get conjugated when we reverse the orientation. In this paper we…

This paper considers how many conjugacy classes of reflections a map can have, under various transitivity conditions. It is shown that for vertex- and for face-transitive maps there is no restriction on their number or size, whereas…

We show that the topological entropy is monotonic for unimodal interval maps which are obtained from the restriction of quadratic rational maps with real coefficients. This is done by ruling out the existence of certain post-critical curves…

We prove strong statistical stability of a large class of one-dimensional maps which may have an arbitrary finite number of discontinuities and of non-degenerate critical points and/or singular points with infinite derivative, and satisfy…

We prove the existence of equilibrium states for geometric potentials in a class of piecewise weakly convex interval maps. This class includes systems with indifferent fixed points and non-Markov partitions. Under additional hypotheses we…

Expanding maps with indifferent fixed points, a.k.a. intermittent maps, are popular models in nonlinear dynamics and infinite ergodic theory. We present a simple proof of the exactness of a wide class of expanding maps of [0,1], with…