The aim of this short note is to compute the topological entropy for a family of skew-product maps, whose base is a subshift of finite type, and the fiber maps are homeomorphisms defined in one dimensional spaces. We show that the skew-product map does not increase the topological entropy of the subshift.

We consider hyperbolic sets of saddle type for holomorphic mappings in P. Our main result relates topological entropy on such sets to a normal families condition on local unstable manifolds.

For further studying the theory of multigranulation rough sets (MGRS), we attempt to investigate a new theory on multigranulation rough sets from the topological view in this paper. We firstly explore multigranulation topological rough space and its topological properties by giving some new definitions and theorems. Then, topological granularity and topological entropy are proposed to character...

We study continuous countably-piecewise monotone interval maps and formulate conditions under which these are conjugate to maps of constant slope, particularly when this slope is given by the topological entropy of the map. We confine our investigation to the Markov case and phrase our conditions in the terminology of the Vere-Jones classification of infinite matrices.

This paper considers a Cournot duopoly model assuming isoelastic demand and smooth cost functions with built-in capacity limits. When the firms cannot obtain positive profits they are assumed to choose small "stand-by" outputs rather than closing down, in order to avoid substantial fitting up costs when market conditions turn out more favorable. It is shown that the model provides chaotic behav...

A basic problem in dynamics is to identify systems with positive entropy, i.e., systems which are “chaotic.” While there is a vast collection of results addressing this issue in topological dynamics, the phenomenon of positive entropy remains by and large a mystery within the broader noncommutative domain of C∗-algebraic dynamics. To shed some light on the noncommutative situation we propose a ...

This paper studies cellular automata in two aspects: Ergodic and topological behavior. For ergodic aspect, the formulae of measure-theoretic entropy, topological entropy and topological pressure are given in closed forms and Parry measure is demonstrated to be an equilibrium measure for some potential function. For topological aspect, an example is examined to show that the exhibition of snap-b...

We study damped hyperbolic equations on the infinite line. We show that on the global attracting set G the ε-entropy (per unit length) exists in the topology of W 1,∞. We also show that the topological entropy per unit length of G exists. These results are shown using two main techniques: Bounds in bounded domains in position space and for large momenta, and a novel submultiplicativity argument...

We prove two theorems which extend known results concerning periodic orbits and topological entropy in one-dimensional dynamics. One of these results concerns the adding machine map (also called the odometer map) fα defined on the α-adic adding machine ∆α. We let H(fα) denote the greatest lower bound of the topological entropies of F , taken over all continuous maps F of the interval which cont...

The notion of topological entropy dimension for a Z-action has been introduced to measure the subexponential complexity of zero entropy systems. Given a Z2-action, along with a Z2-entropy dimension, we also consider a finer notion of directional entropy dimension arising from its subactions. The entropy dimension of a Z2-action and the directional entropy dimensions of its subactions satisfy ce...