Related papers: Transitive sensitive subsystems for interval maps
We define weaker forms of topological and measure theoretical equicontinuity for topological dynamical systems and we study their relationships with systems with discrete spectrum and zero sequence entropy. In the topological category we…
A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences $x_{n+1}=F(x_n)$ generated by such maps display…
We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.
We show sensitive dependece on initial condition and dense periodic points imply asymptotic sensitivity, a stronger form of sensitivity, where the deviation happens not just once but infintely many times. As a consequence it follows that…
In this study, Devaney's chaos conditions are revisited within the framework of descriptive proximity. The concepts of descriptive transitivity, the density of descriptive periodic objects, and descriptive sensitivity are defined. The most…
Weak chaos in high-dimensional conservative systems can be characterized through sticky effect induced by invariant structures on chaotic trajectories. Suitable quantities for this characterization are the higher cummulants of the finite…
We prove a random Ruelle--Perron--Frobenius theorem and the existence of relative equilibrium states for a class of random open and closed interval maps, without imposing transitivity requirements, such as mixing and covering conditions,…
Recently, in connection with C*-algebra theory, the first author and Danilo Royer introduced ultragraph shift spaces. In this paper we define a family of metrics for the topology in such spaces, and use these metrics to study the existence…
We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
The notion of Li-Yorke sensitivity has been studied extensively in the case of topological dynamical systems. We introduce a measurable version of Li-Yorke sensitivity, for nonsingular (and measure-preserving) dynamical systems, and compare…
Maps that are not completely positive (CP) are often useful to describe the dynamics of open systems. An apparent violation of complete positivity can occur because there are prior correlations of the principal system with the environment,…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
We consider a class $\mathcal{F}$ of Markov multi-maps on the unit interval. Any multi-map gives rise to a space of trajectories, which is a closed, shift-invariant subset of $[0,1]^{\mathbb{Z}_+}$. For a multi-map in $\mathcal{F}$, we show…
In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a…
We define variational properties for dynamical systems with subexponential complexity, and study these properties in certain specific examples. By computing the value of slow entropy directly, we show that some subshifts are not…
The topological entropy of a continuous self-map of a compact metric space can be defined in several distinct ways; when the space is not assumed compact, these definitions can lead to distinct invariants. The original, purely topological…
Hierarchy of one-parameter families of chaotic maps with an invariant measure have been introduced, where their appropriate coupling has lead to the generation of some coupled chaotic maps with an invariant measure. It is shown that these…
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes…