Open AccessOn the maximal invariant set for the map x2 – 2 restricted to intervals
Author(s) -
Dušan Bednařı́k,
Diego Marques,
Carlos Gustavo Moreira,
Pavel Trojovský
Publication year - 2021
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-2021-02-0018
Subject(s) - invariant (physics) , mathematics , chaotic , quadratic equation , class (philosophy) , discrete mathematics , interval (graph theory) , combinatorics , pure mathematics , computer science , artificial intelligence , geometry , mathematical physics
In this paper, we study the maximal invariant set of a quadratic family related to a class of unimodal maps. This family is very important and have direct application in many branches of science. In particular, we characterize when the maximal invariant of f(x) = x2 − 2 (restricted to an interval) has a chaotic behavior.