Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

# Advanced Search

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 0758.58019
Banks, J.; Brooks, J.; Cairns, G.; Davis, G.; Stacey, P.
On Devaney's definition of chaos.
(English)
[J] Am. Math. Mon. 99, No.4, 332-334 (1992). ISSN 0002-9890

Although there has been no universally accepted mathematical definition of chaos, R. L. Devaney isolated three components as being its essential features: according to his definition [{\it R. L. Devaney}, An introduction to chaotic dynamical systems, 2nd ed. (1989; Zbl 0695.58002)], a continuous map $f: X\to X$, where $X$ is a metric space, is said to be chaotic on $X$ if 1) $f$ is transitive, 2) the periodic points of $f$ are dense in $X$, 3) $f$ has sensitive dependence on initial conditions. The aim of the paper is to prove the following result: if $f: X\to X$ is transitive and has dense periodic points then $f$ has sensitive dependence on initial conditions.
[I.Oprea (Bucureşti)]
MSC 2000:
*37D45 Strange attractors, chaotic dynamics

Keywords: dynamical system; chaos; dependence on initial conditions

Citations: Zbl 0695.58002

Login Username: Password:

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster