Topological Sequence Entropy

Entropy operator for continuous dynamical systems of finite topological entropy

In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

Topological Sequence Entropy for Maps of the Interval

A result by Franzová and Smı́tal shows that a continuous map of the interval into itself is chaotic if and only if its topological sequence entropy relative to a suitable increasing sequence of nonnegative integers is positive. In the present paper we prove that for any increasing sequence of nonnegative integers there exists a chaotic continuous map with zero topological sequence entropy relati...

Statistical Convergent Topological Sequence Entropy Maps of the Circle

A continuous map f of the interval is chaotic iff there is an increasing of nonnegative integers T such that the topological sequence entropy of f relative to T, hT(f), is positive [4]. On the other hand, for any increasing sequence of nonnegative integers T there is a chaotic map f of the interval such that hT(f)=0 [7]. We prove that the same results hold for maps of the circle. We also prove ...

ENTROPY OF GEODESIC FLOWS ON SUBSPACES OF HECKE SURFACE WITH ARITHMETIC CODE

There are dierent ways to code the geodesic flows on surfaces with negative curvature. Such code spaces give a useful tool to verify the dynamical properties of geodesic flows. Here we consider special subspaces of geodesic flows on Hecke surface whose arithmetic codings varies on a set with innite alphabet. Then we will compare the topological complexity of them by computing their topological ...

QSPR Modeling of Heat Capacity, Thermal Energy and Entropy of Aliphatic Aldehydes by using Topological Indices and MLR Method

Topological sequence entropy for maps of the circle

A continuous map f of the interval is chaotic iff there is an increasing sequence of nonnegative integers T such that the topological sequence entropy of f relative to T , hT (f), is positive ([FS]). On the other hand, for any increasing sequence of nonnegative integers T there is a chaotic map f of the interval such that hT (f) = 0 ([H]). We prove that the same results hold for maps of the cir...