We prove that every C1 diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub’s entropy conjecture: the entropy is bounded from below by the spectral radius in homology. Moreover, they admit principal symbolic extensions, and the topological entropy and metrical entropy vary continuously wit...

Let X be a compact metric space and [Formula: see text] a continuous map. Considering the space [Formula: see text] of all nonempty fuzzy sets on X endowed with the levelwise topology, we proved that its g-fuzzification is turbulent or erratic if the given system f is turbulent or erratic correspondingly and f is [Formula: see text]-expansive if and only if its g-fuzzification is [Formula: see ...

In this paper, we prove that any C1-persistently positively expansive map is expanding. This improves a result due to Sakai (Sakai 2004).

Abs t rac t . This paper describes a new technique for reducing the complexity of algorithms, such as those used in digital signal processing~ using a genetic algorithm (GA). The method, referred to as expansive coding, is a representation methodology which makes complicated combinatorim optimisation tasks easier to solve for a. GA. Using this technique, the representation, operators and fitnes...