On the definition of chaos
Abstract
Five definitions of chaos used in discrete dynamical systems are reviewed. Their invariance with respect to topological conjugacy is proved. It is shown that the socalled shadowing property is the most basic of the five definitions: it implies chaos in the sense of cointossing, chaos in the sense of Devaney, chaos in the sense of LiYorke and chaos in the sense of Bernoulli. The following examples are treated or indicated: Torus automorphisms, snapback repellors, transversal homoclinic points. In addition, extensions to nonautonomous discrete dynamical systems with implications for nonperiodic differential equations are described.
 Publication:

Zeitschrift Angewandte Mathematik und Mechanik
 Pub Date:
 1989
 DOI:
 10.1002/zamm.19890690703
 Bibcode:
 1989ZaMM...69..175K
 Keywords:

 Chaos;
 Dynamical Systems;
 Topology;
 Differential Equations;
 Geometry;
 Mathematical Models;
 Orbital Mechanics;
 Poincare Problem;
 Physics (General)