Dendrite (mathematics)
Appearance
In mathematics, a dendrite is a certain type of topological space that may be characterized either as a locally connected dendroid or equivalently as a locally connected continuum that contains no simple closed curves.[1]
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/07/Dendrite_julia.png/220px-Dendrite_julia.png)
Importance
Dendrites may be used to model certain types of Julia set.[2] For example, if 0 is pre-periodic, but not periodic, under the function , then the Julia set of is a dendrite.[3]
References
- ^ Whyburn, Gordon Thomas (1942), Analytic Topology, American Mathematical Society Colloquium Publications, vol. 28, New York: American Mathematical Society, p. 88, MR 0007095.
- ^ Carleson, Lennart; Gamelin, Theodore W. (1993), Complex Dynamics, Universitext, vol. 69, Springer, p. 94, ISBN 9780387979427.
- ^ Devaney, Robert L. (1989), An Introduction to Chaotic Dynamical Systems, Studies in Nonlinearity, Addison-Wesley Publishing Company, p. 294, MR 1046376.
See also
![](http://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png)
Wikimedia Commons has media related to Dendrite Julia sets.
- Misiurewicz point
- Real tree, a related concept defined using metric spaces instead of topological spaces
- Dendroid (topology) and unicoherent space, two more general types of tree-like topological space