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.
Dendrites may be used to model certain types of Julia set. For example, if 0 is pre-periodic, but not periodic, under the function , then the Julia set of is a dendrite.
- Whyburn, Gordon Thomas (1942), Analytic Topology, American Mathematical Society Colloquium Publications, 28, New York: American Mathematical Society, p. 88, MR 0007095.
- Carleson, Lennart; Gamelin, Theodore W. (1993), Complex Dynamics, Universitext, 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.
|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