相关论文: Semiconjugacy to a map of a constant slope

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…

For any transitive piecewise monotonic map for which the set of periodic measures is dense in the set of ergodic invariant measures (such as monotonic mod one transformations and piecewise monotonic maps with two monotonic pieces), we show…

We characterize disjoint hypercyclic sequences of wedge operators. Also, we give some sufficient conditions for a sequence of the dual wedge operators to be disjoint topologically transitive. Finally, we give some concrete examples and…

For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of their position. By assuming a global…

Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…

In this paper, various chaotic properties and their relationships for interval maps are discussed. It is shown that the proximal relation is an equivalence relation for any zero entropy interval map. The structure of the set of…

We completely classify the orientable infinite-type surfaces $S$ such that $\operatorname{PMap}(S)$, the pure mapping class group, has automatic continuity. This classification includes surfaces with noncompact boundary. In the case of…

The goal of this article is to study how combinatorial equivalence implies topological conjugacy. For that, we introduce the concept of kneading sequences for nonautonomous discrete dynamical systems and show that these sequences are a…

Let $g$ and $h$ be transcendental entire functions and let $f$ be a continuous map of the complex plane into itself with $f\circ g=h\circ f.$ Then $g$ and $h$ are said to be semiconjugated by $f$ and $f$ is called a semiconjugacy. We…

In this paper we will develop a very general approach which shows that critical relations of holomorphic maps on the complex plane unfold transversally in a positively oriented way. We will mainly illustrate this approach to obtain…

In this paper, we give a complete topological and smooth classification of non-invertible Anosov maps on torus. We show that two non-invertible Anosov maps on torus are topologically conjugate if and only if their corresponding periodic…

We compare a piecewise linear map with constant slope beta>1 and a piecewise linear map with constant slope -beta. These maps are called the positive and negative beta-transformations. We show that for a certain set of beta's, the…

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.

The topological classification of the inner mappings on the fully invariant regular components of the wandering set with a special attracting boundary up to the topological conjugacy is defined in terms of distinguishing graph. Two inner…

In this paper, we focus attention on extending the topological conjugacy of adding machine maps and minimal systems to iterated function systems. We provide necessary and sufficient conditions for an iterated function system to be…

In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…

The dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences. The use of intermittent maps, as opposed to other simple chaotic maps, is particularly suited for the production of long range…

We show that attractors are semicontinuous for closed relations on compact Hausdorff spaces. Semicontinuity is what guarantees that small changes to a system do not result in massive growth of certain features, notably attractors. That is,…

For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…

We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. The algorithm is obtained by the sign analysis of the itineraries of…