相关论文: Topological entropy, sets of periods and transitiv…

In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…

The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…

Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…

We prove that a zero topological entropy continuous tree map always displays zero topological sequence entropy when it is restricted to its non-wandering and chain recurrent sets. In addition, we show that a similar result is not possible…

We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the well-known notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of…

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…

Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their…

Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…

For any discrete time dynamical system with a rational evolution, we define an entropy, which is a global index of complexity for the evolution map. We analyze its basic properties and its relations to the singularities and the…

We consider the family of piecewise linear maps $F(x,y)=\left(|x| - y + a, x - |y| + b\right),$ where $(a,b)\in \R^2$. In previous work, we identified a novel phenomenon: certain maps of this class possess one-dimensional invariant sets,…

It is well known that a continuous piecewise monotone interval map with positive topological entropy is semiconjugate to a map of a constant slope and the same entropy, and if it is additionally transitive then this semiconjugacy is…

The topological entropy of piecewise affine maps is studied. It is shown that singularities may contribute to the entropy only if there is angular expansion and we bound the entropy via the expansion rates of the map. As a corollary we…

Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…

For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense…

We use the complexity function of an invariant, not necessary closed, subset of a two-sided shift space to compute the polynomial entropy of the induced dynamics on the hyperspace of continua for certain one-dimensional dynamical systems.…

A temporal graph is a graph whose edges only appear at certain points in time. Reachability in these graphs is defined in terms of paths that traverse the edges in chronological order (temporal paths). This form of reachability is neither…

We study dynamics of continuous maps on compact metrizable spaces containing a free interval (i.e., an open subset homeomorphic to an open interval). A special attention is paid to relationships between topological transitivity, weak and…

We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…

Quantifying the complexity of large graphs requires measures that extend beyond predefined structural features and scale efficiently with graph size. This work adopts a generative perspective, modeling large networks as exchangeable graphs…