In this work we introduce a concept of expansiveness for actions connected Lie groups. We study some its properties and investigate implications expansiveness. the centralizer expansive CW-expansiveness pseudo-group actions. As an application, prove positiveness geometric entropy foliations group

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...